/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 69 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 17.3 s] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 53 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 335 ms] (18) CdtProblem (19) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (20) CdtProblem (21) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CdtProblem (23) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (24) CdtProblem (25) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (26) CdtProblem (27) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CdtProblem (29) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (30) CdtProblem (31) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (32) CdtProblem (33) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CdtProblem (35) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtForwardInstantiationProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (70) CdtProblem (71) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 53 ms] (74) CdtProblem (75) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (76) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(x1)) -> 2(2(1(x1))) 1(1(0(x1))) -> 1(2(2(1(x1)))) 0(2(2(0(0(1(1(x1))))))) -> 1(0(2(2(2(2(2(1(2(1(1(x1))))))))))) 1(0(0(2(1(0(1(x1))))))) -> 0(2(2(2(1(0(2(2(x1)))))))) 0(1(1(0(0(2(0(2(0(1(2(0(x1)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(x1))))))))))))) 1(2(1(0(1(2(2(0(1(1(1(1(x1)))))))))))) -> 1(2(1(2(1(0(2(0(2(2(1(2(0(x1))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(x1))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(x1))))))))))))))))))) 1(0(0(2(0(1(1(1(1(1(2(2(0(0(2(1(1(x1))))))))))))))))) -> 2(1(2(2(2(2(1(1(2(0(2(2(1(1(1(2(0(1(x1)))))))))))))))))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(x1)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(x1))))))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(x1))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(x1))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(x1))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(x1))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(x1)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(x1))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(x1)))))))))))))))))))))) 1(1(0(2(0(1(0(1(1(0(1(2(2(1(0(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(2(2(0(2(0(0(0(2(1(2(0(1(1(1(0(0(1(2(2(0(0(2(1(2(0(2(1(x1))))))))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(x1))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(x1)))))))))))))))))))))))))) 1(2(1(2(2(0(1(1(0(1(0(2(1(0(1(0(0(1(1(1(2(0(1(0(1(x1))))))))))))))))))))))))) -> 0(2(0(2(1(0(1(0(1(2(1(2(1(2(0(2(0(2(1(0(1(0(0(0(2(1(0(2(x1)))))))))))))))))))))))))))) 1(2(0(1(1(0(0(2(1(0(2(2(1(2(0(0(2(2(0(2(2(0(0(0(1(1(x1)))))))))))))))))))))))))) -> 2(0(0(0(2(2(2(0(0(2(1(0(2(2(0(0(2(1(2(2(1(1(0(0(2(0(0(1(0(0(x1)))))))))))))))))))))))))))))) 1(2(2(0(1(0(2(1(1(0(0(0(0(0(0(0(1(0(0(0(1(2(2(1(2(2(2(x1))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(0(2(2(0(0(0(0(2(1(0(0(0(1(0(2(2(2(0(0(0(2(1(x1))))))))))))))))))))))))))))) 1(2(2(0(1(1(2(1(0(1(0(2(1(1(2(2(2(1(1(1(2(0(2(0(0(1(1(x1))))))))))))))))))))))))))) -> 2(2(1(0(0(2(2(1(2(1(2(2(2(2(1(2(2(2(1(0(2(1(2(0(0(0(0(1(2(1(0(x1))))))))))))))))))))))))))))))) 1(1(0(1(1(0(1(2(0(0(0(1(0(1(0(0(2(2(0(1(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) -> 1(2(1(1(2(2(1(1(0(2(0(0(1(2(0(0(0(1(2(1(1(0(2(0(0(2(1(0(1(1(x1)))))))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(x1))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(x1)))))))))))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(x1))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(x1)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(x1)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(x1)))))))))))))))))))))))))))))) 0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(x1)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(x1))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(x1))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(x1))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(x1))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(x1))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(x1)))))))))))))))))))))))))))))))) 0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(x1)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(x1)))))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(x1)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(x1))))))))))))))))))))))))))))))))) 0(2(1(0(1(1(2(0(1(2(1(2(2(0(2(1(1(1(0(1(1(0(2(0(1(1(2(2(1(2(0(2(2(x1))))))))))))))))))))))))))))))))) -> 2(1(2(2(2(2(2(0(2(1(1(1(1(2(0(0(0(2(0(0(2(2(1(1(0(0(1(1(2(1(0(2(1(0(2(x1))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(0(0(0(2(0(0(2(0(2(1(0(2(1(0(1(2(2(0(1(2(0(0(1(0(1(x1))))))))))))))))))))))))))))))))) -> 0(0(0(2(1(0(2(1(0(2(1(0(2(1(1(2(2(2(1(2(0(0(2(0(0(2(1(1(1(0(2(2(1(0(1(x1))))))))))))))))))))))))))))))))))) 0(2(0(1(0(1(0(2(0(0(2(0(2(1(0(0(0(0(0(1(0(2(2(2(0(0(2(0(2(1(1(0(2(2(x1)))))))))))))))))))))))))))))))))) -> 2(2(1(2(0(1(2(0(1(2(2(2(1(1(2(2(2(1(1(2(1(2(2(0(2(2(0(2(1(0(2(0(2(2(0(x1))))))))))))))))))))))))))))))))))) 0(2(2(2(0(0(1(2(0(2(0(0(1(1(2(1(1(0(1(2(0(1(0(1(2(0(2(1(0(0(1(1(2(0(x1)))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(0(2(1(0(0(2(1(2(2(2(1(0(1(0(0(0(0(2(0(1(1(0(2(0(0(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))) 0(0(0(1(0(2(2(2(0(1(0(0(2(2(2(1(1(0(1(0(2(1(0(0(0(0(1(0(1(2(0(0(2(1(0(x1))))))))))))))))))))))))))))))))))) -> 1(2(2(0(1(2(1(1(2(2(0(2(0(0(2(1(0(0(0(2(1(2(0(2(1(1(2(2(2(2(2(2(2(2(2(1(x1)))))))))))))))))))))))))))))))))))) 0(0(2(2(2(1(1(2(2(2(1(2(1(0(1(0(0(2(2(1(2(1(1(1(1(1(0(2(2(0(1(1(2(1(2(x1))))))))))))))))))))))))))))))))))) -> 0(2(2(2(1(0(0(2(2(0(0(0(0(2(2(2(1(0(2(2(1(0(2(1(2(1(0(2(2(1(2(2(2(0(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))) 0(1(2(1(0(2(1(0(2(0(0(1(1(1(1(1(0(0(0(0(2(1(0(2(1(0(1(2(1(1(2(2(0(1(1(x1))))))))))))))))))))))))))))))))))) -> 2(0(1(1(0(1(2(1(1(1(2(1(2(2(0(2(1(0(1(1(1(1(1(2(1(2(0(2(1(1(1(1(0(0(1(2(x1)))))))))))))))))))))))))))))))))))) 1(1(0(1(1(1(1(2(0(0(0(0(0(0(2(1(0(0(1(2(0(1(1(0(2(0(0(0(2(1(2(1(2(1(0(x1))))))))))))))))))))))))))))))))))) -> 1(0(0(0(0(1(0(2(0(1(1(2(0(2(0(2(0(2(0(0(0(0(2(1(2(2(2(2(2(1(0(0(1(0(0(2(0(x1))))))))))))))))))))))))))))))))))))) 0(1(2(2(0(1(1(2(1(2(0(1(1(0(0(1(1(0(0(0(1(1(0(1(1(1(1(2(1(1(1(1(1(2(0(1(x1)))))))))))))))))))))))))))))))))))) -> 1(2(0(1(2(0(2(2(2(0(2(1(2(0(2(2(2(1(2(1(2(2(1(2(1(2(2(0(2(0(1(0(1(0(0(0(2(1(0(2(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) 1(1(2(0(1(0(1(0(1(1(0(2(0(2(2(1(0(2(0(0(2(0(1(2(2(0(2(0(0(0(0(1(2(2(0(1(x1)))))))))))))))))))))))))))))))))))) -> 2(1(1(2(0(0(1(2(2(2(1(0(1(2(0(2(1(1(1(0(1(1(1(1(1(2(2(2(2(1(2(0(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(x1)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(x1)))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(1(2(0(1(2(2(2(0(2(0(2(0(0(2(2(0(0(0(0(2(0(0(0(0(2(2(0(1(1(1(0(1(x1))))))))))))))))))))))))))))))))))))) -> 1(2(1(1(1(1(2(2(0(0(2(1(1(1(2(0(2(2(0(0(1(2(0(1(2(0(1(1(0(1(2(2(0(2(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))) 0(0(0(2(0(0(1(0(0(1(1(1(2(0(0(1(2(0(0(0(0(1(1(0(1(0(2(1(1(1(0(0(0(2(1(0(0(x1))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(2(0(2(0(0(2(1(2(2(1(2(2(2(0(2(2(0(2(0(0(2(1(2(2(2(0(2(1(2(0(2(0(2(1(0(1(1(x1))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(2(2(1(0(0(1(0(1(1(0(0(2(1(1(2(1(1(2(2(2(2(0(0(1(0(1(0(0(1(1(2(2(1(x1))))))))))))))))))))))))))))))))))))) -> 1(2(0(0(2(2(1(1(2(2(1(0(1(2(0(2(1(1(1(2(2(0(0(1(0(2(2(2(0(2(2(2(2(1(2(1(2(2(0(0(x1)))))))))))))))))))))))))))))))))))))))) 1(2(1(0(0(1(1(2(2(0(0(1(0(1(2(1(1(1(0(1(2(0(2(1(1(1(1(1(0(1(2(2(2(0(2(0(2(x1))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(2(0(0(2(2(0(2(2(1(2(2(2(1(0(0(1(1(0(0(2(0(2(0(2(1(1(1(1(1(2(1(0(1(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))) 1(2(2(1(2(1(0(0(1(2(2(1(0(0(1(2(1(0(0(1(0(0(2(1(0(1(0(2(0(2(1(0(0(0(2(0(1(x1))))))))))))))))))))))))))))))))))))) -> 2(0(0(2(1(1(2(1(2(1(1(1(1(0(1(0(2(0(1(2(1(2(2(1(2(2(1(2(2(1(2(1(2(2(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(0(1(2(0(0(0(0(0(2(2(1(0(0(2(1(0(0(2(2(0(2(0(0(1(2(0(0(1(2(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(1(1(1(0(0(1(2(0(2(2(2(1(1(0(2(0(1(1(1(2(2(1(1(0(1(2(1(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(1(1(1(1(0(0(2(0(2(1(0(0(2(1(0(1(1(0(2(2(0(2(1(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(2(0(1(1(2(2(0(2(1(1(2(2(2(0(1(0(2(2(1(2(2(0(0(2(1(2(1(2(2(2(2(0(2(2(1(0(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))) 1(0(2(0(1(1(2(1(1(0(1(2(1(0(1(0(1(1(0(2(1(0(1(0(2(1(0(1(1(0(1(1(0(2(1(0(1(2(x1)))))))))))))))))))))))))))))))))))))) -> 1(2(1(1(2(0(1(2(1(0(2(0(0(0(2(2(0(2(2(2(1(2(0(1(0(2(0(1(2(1(2(1(2(1(1(1(2(2(0(0(0(2(2(x1))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(2(0(0(0(0(0(0(2(1(2(1(1(1(1(2(2(1(0(0(0(0(1(1(1(1(1(1(2(1(2(0(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(2(2(0(0(2(1(0(1(1(0(2(1(2(1(0(2(1(0(0(1(0(1(0(2(0(2(1(1(2(2(0(0(2(2(1(2(x1)))))))))))))))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(0(0(2(1(1(0(0(1(0(0(1(0(0(0(1(2(2(0(1(0(1(0(0(0(2(2(1(x1))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(0(1(1(2(1(2(2(1(1(2(2(0(0(0(1(1(1(2(1(2(2(2(0(0(1(2(2(2(1(2(2(2(0(2(2(2(1(2(1(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(2(1(2(1(0(0(1(1(0(1(0(1(2(0(1(1(1(1(1(1(0(0(1(1(1(0(2(1(2(2(0(0(2(0(1(2(0(x1)))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(0(0(1(1(2(2(1(0(0(1(2(0(2(1(1(2(1(0(0(0(2(1(2(2(2(1(0(0(2(2(0(0(1(1(0(2(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) 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1(2(1(0(0(0(0(2(1(1(1(0(0(2(1(1(1(0(1(1(1(0(0(0(2(0(2(1(0(0(2(1(2(0(2(1(1(2(2(2(0(0(2(1(2(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(1(0(0(2(1(2(1(1(0(2(1(1(0(0(2(0(1(1(1(0(0(0(0(0(1(0(0(2(1(1(1(0(1(0(1(1(2(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(2(2(1(2(2(2(0(2(1(2(1(1(0(2(1(1(1(2(2(0(1(1(1(0(0(1(1(1(0(1(1(2(1(0(2(0(2(1(2(2(1(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(0(2(2(0(2(1(1(1(2(2(0(0(2(2(2(0(0(1(1(0(0(2(0(0(2(2(0(0(0(2(2(0(1(1(1(0(2(0(1(2(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(0(0(2(2(0(0(1(0(2(2(0(0(2(2(0(2(1(0(2(2(0(2(2(1(0(2(2(2(2(0(1(1(2(0(2(2(1(0(0(0(2(0(2(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(1(1(1(0(0(2(0(1(2(0(2(0(0(2(0(2(2(0(1(0(1(1(2(0(1(1(2(0(0(2(1(0(0(1(2(2(1(2(0(2(0(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(1(1(1(0(0(0(0(0(2(2(2(1(2(2(0(2(2(0(0(2(1(1(0(1(2(2(0(1(0(1(1(0(2(1(1(0(1(2(1(2(0(0(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(x1)) -> 2(2(1(x1))) 1(1(0(x1))) -> 1(2(2(1(x1)))) 0(2(2(0(0(1(1(x1))))))) -> 1(0(2(2(2(2(2(1(2(1(1(x1))))))))))) 1(0(0(2(1(0(1(x1))))))) -> 0(2(2(2(1(0(2(2(x1)))))))) 0(1(1(0(0(2(0(2(0(1(2(0(x1)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(x1))))))))))))) 1(2(1(0(1(2(2(0(1(1(1(1(x1)))))))))))) -> 1(2(1(2(1(0(2(0(2(2(1(2(0(x1))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(x1))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(x1))))))))))))))))))) 1(0(0(2(0(1(1(1(1(1(2(2(0(0(2(1(1(x1))))))))))))))))) -> 2(1(2(2(2(2(1(1(2(0(2(2(1(1(1(2(0(1(x1)))))))))))))))))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(x1)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(x1))))))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(x1))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(x1))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(x1))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(x1))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(x1)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(x1))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(x1)))))))))))))))))))))) 1(1(0(2(0(1(0(1(1(0(1(2(2(1(0(1(1(2(0(1(2(1(2(x1))))))))))))))))))))))) -> 2(2(2(2(0(2(0(0(0(2(1(2(0(1(1(1(0(0(1(2(2(0(0(2(1(2(0(2(1(x1))))))))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(x1))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(x1)))))))))))))))))))))))))) 1(2(1(2(2(0(1(1(0(1(0(2(1(0(1(0(0(1(1(1(2(0(1(0(1(x1))))))))))))))))))))))))) -> 0(2(0(2(1(0(1(0(1(2(1(2(1(2(0(2(0(2(1(0(1(0(0(0(2(1(0(2(x1)))))))))))))))))))))))))))) 1(2(0(1(1(0(0(2(1(0(2(2(1(2(0(0(2(2(0(2(2(0(0(0(1(1(x1)))))))))))))))))))))))))) -> 2(0(0(0(2(2(2(0(0(2(1(0(2(2(0(0(2(1(2(2(1(1(0(0(2(0(0(1(0(0(x1)))))))))))))))))))))))))))))) 1(2(2(0(1(0(2(1(1(0(0(0(0(0(0(0(1(0(0(0(1(2(2(1(2(2(2(x1))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(0(2(2(0(0(0(0(2(1(0(0(0(1(0(2(2(2(0(0(0(2(1(x1))))))))))))))))))))))))))))) 1(2(2(0(1(1(2(1(0(1(0(2(1(1(2(2(2(1(1(1(2(0(2(0(0(1(1(x1))))))))))))))))))))))))))) -> 2(2(1(0(0(2(2(1(2(1(2(2(2(2(1(2(2(2(1(0(2(1(2(0(0(0(0(1(2(1(0(x1))))))))))))))))))))))))))))))) 1(1(0(1(1(0(1(2(0(0(0(1(0(1(0(0(2(2(0(1(1(1(0(2(1(0(1(0(x1)))))))))))))))))))))))))))) -> 1(2(1(1(2(2(1(1(0(2(0(0(1(2(0(0(0(1(2(1(1(0(2(0(0(2(1(0(1(1(x1)))))))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(x1))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(x1)))))))))))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(x1))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(x1)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(x1)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(x1)))))))))))))))))))))))))))))) 0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(x1)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(x1)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(x1))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(x1))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(x1))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(x1))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(x1))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(x1)))))))))))))))))))))))))))))))) 0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(x1)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(x1)))))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(x1)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(x1))))))))))))))))))))))))))))))))) 0(2(1(0(1(1(2(0(1(2(1(2(2(0(2(1(1(1(0(1(1(0(2(0(1(1(2(2(1(2(0(2(2(x1))))))))))))))))))))))))))))))))) -> 2(1(2(2(2(2(2(0(2(1(1(1(1(2(0(0(0(2(0(0(2(2(1(1(0(0(1(1(2(1(0(2(1(0(2(x1))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(0(0(0(2(0(0(2(0(2(1(0(2(1(0(1(2(2(0(1(2(0(0(1(0(1(x1))))))))))))))))))))))))))))))))) -> 0(0(0(2(1(0(2(1(0(2(1(0(2(1(1(2(2(2(1(2(0(0(2(0(0(2(1(1(1(0(2(2(1(0(1(x1))))))))))))))))))))))))))))))))))) 0(2(0(1(0(1(0(2(0(0(2(0(2(1(0(0(0(0(0(1(0(2(2(2(0(0(2(0(2(1(1(0(2(2(x1)))))))))))))))))))))))))))))))))) -> 2(2(1(2(0(1(2(0(1(2(2(2(1(1(2(2(2(1(1(2(1(2(2(0(2(2(0(2(1(0(2(0(2(2(0(x1))))))))))))))))))))))))))))))))))) 0(2(2(2(0(0(1(2(0(2(0(0(1(1(2(1(1(0(1(2(0(1(0(1(2(0(2(1(0(0(1(1(2(0(x1)))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(0(2(1(0(0(2(1(2(2(2(1(0(1(0(0(0(0(2(0(1(1(0(2(0(0(1(0(1(0(0(x1))))))))))))))))))))))))))))))))))) 0(0(0(1(0(2(2(2(0(1(0(0(2(2(2(1(1(0(1(0(2(1(0(0(0(0(1(0(1(2(0(0(2(1(0(x1))))))))))))))))))))))))))))))))))) -> 1(2(2(0(1(2(1(1(2(2(0(2(0(0(2(1(0(0(0(2(1(2(0(2(1(1(2(2(2(2(2(2(2(2(2(1(x1)))))))))))))))))))))))))))))))))))) 0(0(2(2(2(1(1(2(2(2(1(2(1(0(1(0(0(2(2(1(2(1(1(1(1(1(0(2(2(0(1(1(2(1(2(x1))))))))))))))))))))))))))))))))))) -> 0(2(2(2(1(0(0(2(2(0(0(0(0(2(2(2(1(0(2(2(1(0(2(1(2(1(0(2(2(1(2(2(2(0(2(1(1(1(x1)))))))))))))))))))))))))))))))))))))) 0(1(2(1(0(2(1(0(2(0(0(1(1(1(1(1(0(0(0(0(2(1(0(2(1(0(1(2(1(1(2(2(0(1(1(x1))))))))))))))))))))))))))))))))))) -> 2(0(1(1(0(1(2(1(1(1(2(1(2(2(0(2(1(0(1(1(1(1(1(2(1(2(0(2(1(1(1(1(0(0(1(2(x1)))))))))))))))))))))))))))))))))))) 1(1(0(1(1(1(1(2(0(0(0(0(0(0(2(1(0(0(1(2(0(1(1(0(2(0(0(0(2(1(2(1(2(1(0(x1))))))))))))))))))))))))))))))))))) -> 1(0(0(0(0(1(0(2(0(1(1(2(0(2(0(2(0(2(0(0(0(0(2(1(2(2(2(2(2(1(0(0(1(0(0(2(0(x1))))))))))))))))))))))))))))))))))))) 0(1(2(2(0(1(1(2(1(2(0(1(1(0(0(1(1(0(0(0(1(1(0(1(1(1(1(2(1(1(1(1(1(2(0(1(x1)))))))))))))))))))))))))))))))))))) -> 1(2(0(1(2(0(2(2(2(0(2(1(2(0(2(2(2(1(2(1(2(2(1(2(1(2(2(0(2(0(1(0(1(0(0(0(2(1(0(2(1(2(0(1(x1)))))))))))))))))))))))))))))))))))))))))))) 1(1(2(0(1(0(1(0(1(1(0(2(0(2(2(1(0(2(0(0(2(0(1(2(2(0(2(0(0(0(0(1(2(2(0(1(x1)))))))))))))))))))))))))))))))))))) -> 2(1(1(2(0(0(1(2(2(2(1(0(1(2(0(2(1(1(1(0(1(1(1(1(1(2(2(2(2(1(2(0(2(0(2(1(1(2(2(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(x1)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(x1)))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(1(2(0(1(2(2(2(0(2(0(2(0(0(2(2(0(0(0(0(2(0(0(0(0(2(2(0(1(1(1(0(1(x1))))))))))))))))))))))))))))))))))))) -> 1(2(1(1(1(1(2(2(0(0(2(1(1(1(2(0(2(2(0(0(1(2(0(1(2(0(1(1(0(1(2(2(0(2(1(1(0(0(1(x1))))))))))))))))))))))))))))))))))))))) 0(0(0(2(0(0(1(0(0(1(1(1(2(0(0(1(2(0(0(0(0(1(1(0(1(0(2(1(1(1(0(0(0(2(1(0(0(x1))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(2(0(2(0(0(2(1(2(2(1(2(2(2(0(2(2(0(2(0(0(2(1(2(2(2(0(2(1(2(0(2(0(2(1(0(1(1(x1))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(2(2(1(0(0(1(0(1(1(0(0(2(1(1(2(1(1(2(2(2(2(0(0(1(0(1(0(0(1(1(2(2(1(x1))))))))))))))))))))))))))))))))))))) -> 1(2(0(0(2(2(1(1(2(2(1(0(1(2(0(2(1(1(1(2(2(0(0(1(0(2(2(2(0(2(2(2(2(1(2(1(2(2(0(0(x1)))))))))))))))))))))))))))))))))))))))) 1(2(1(0(0(1(1(2(2(0(0(1(0(1(2(1(1(1(0(1(2(0(2(1(1(1(1(1(0(1(2(2(2(0(2(0(2(x1))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(2(0(0(2(2(0(2(2(1(2(2(2(1(0(0(1(1(0(0(2(0(2(0(2(1(1(1(1(1(2(1(0(1(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))) 1(2(2(1(2(1(0(0(1(2(2(1(0(0(1(2(1(0(0(1(0(0(2(1(0(1(0(2(0(2(1(0(0(0(2(0(1(x1))))))))))))))))))))))))))))))))))))) -> 2(0(0(2(1(1(2(1(2(1(1(1(1(0(1(0(2(0(1(2(1(2(2(1(2(2(1(2(2(1(2(1(2(2(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(0(1(2(0(0(0(0(0(2(2(1(0(0(2(1(0(0(2(2(0(2(0(0(1(2(0(0(1(2(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(1(1(1(0(0(1(2(0(2(2(2(1(1(0(2(0(1(1(1(2(2(1(1(0(1(2(1(1(2(1(2(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(1(1(1(1(0(0(2(0(2(1(0(0(2(1(0(1(1(0(2(2(0(2(1(2(0(0(2(0(0(x1)))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(2(0(1(1(2(2(0(2(1(1(2(2(2(0(1(0(2(2(1(2(2(0(0(2(1(2(1(2(2(2(2(0(2(2(1(0(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))) 1(0(2(0(1(1(2(1(1(0(1(2(1(0(1(0(1(1(0(2(1(0(1(0(2(1(0(1(1(0(1(1(0(2(1(0(1(2(x1)))))))))))))))))))))))))))))))))))))) -> 1(2(1(1(2(0(1(2(1(0(2(0(0(0(2(2(0(2(2(2(1(2(0(1(0(2(0(1(2(1(2(1(2(1(1(1(2(2(0(0(0(2(2(x1))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(2(0(0(0(0(0(0(2(1(2(1(1(1(1(2(2(1(0(0(0(0(1(1(1(1(1(1(2(1(2(0(2(1(0(1(x1))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(2(2(0(0(2(1(0(1(1(0(2(1(2(1(0(2(1(0(0(1(0(1(0(2(0(2(1(1(2(2(0(0(2(2(1(2(x1)))))))))))))))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(0(0(2(1(1(0(0(1(0(0(1(0(0(0(1(2(2(0(1(0(1(0(0(0(2(2(1(x1))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(0(1(1(2(1(2(2(1(1(2(2(0(0(0(1(1(1(2(1(2(2(2(0(0(1(2(2(2(1(2(2(2(0(2(2(2(1(2(1(2(2(1(x1)))))))))))))))))))))))))))))))))))))))))))))) 0(0(1(2(1(2(1(0(0(1(1(0(1(0(1(2(0(1(1(1(1(1(1(0(0(1(1(1(0(2(1(2(2(0(0(2(0(1(2(0(x1)))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(0(0(1(1(2(2(1(0(0(1(2(0(2(1(1(2(1(0(0(0(2(1(2(2(2(1(0(0(2(2(0(0(1(1(0(2(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) 0(2(2(1(0(1(2(0(1(1(2(2(1(1(0(2(2(0(1(1(0(0(0(0(1(0(0(1(2(0(2(1(1(0(0(0(1(2(2(1(x1)))))))))))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(0(0(1(0(1(2(1(2(1(2(0(2(0(2(0(0(2(2(0(2(1(0(0(2(2(2(1(2(0(1(1(1(0(0(1(0(0(2(x1)))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(1(2(1(0(1(0(2(1(0(2(1(0(2(0(1(2(0(1(2(0(2(2(2(1(2(1(0(2(1(1(1(1(2(2(0(1(x1)))))))))))))))))))))))))))))))))))))))) -> 1(1(0(2(0(2(2(2(0(1(2(2(2(2(0(2(1(0(1(1(2(2(2(2(1(0(1(1(1(2(1(2(1(0(0(2(1(1(0(0(0(x1))))))))))))))))))))))))))))))))))))))))) 0(2(2(0(1(2(1(2(2(0(0(0(1(2(0(1(0(1(1(0(0(0(0(2(1(0(2(1(0(0(1(2(0(0(2(2(1(0(1(1(0(x1))))))))))))))))))))))))))))))))))))))))) -> 1(1(1(2(1(2(2(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(x1))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(x1))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(x1))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(x1)))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(2(2(0(1(1(1(2(0(2(2(0(1(0(2(0(2(0(0(1(0(2(2(2(2(1(1(1(1(2(2(0(0(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(0(2(2(0(2(2(2(0(2(1(2(2(1(1(0(2(2(2(1(0(2(0(2(2(2(0(0(2(1(0(2(0(0(0(0(1(2(2(2(1(2(2(0(2(0(2(0(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(1(1(2(1(0(2(1(1(2(2(0(2(0(0(1(2(0(0(0(0(1(1(2(2(1(1(2(0(2(1(2(1(1(1(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 1(2(2(1(1(0(0(1(2(1(2(0(1(0(0(0(1(1(1(2(2(2(2(1(2(2(1(2(0(0(1(2(0(1(0(1(1(2(2(2(2(0(2(1(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(2(0(2(1(1(2(0(0(0(2(0(1(2(2(2(0(0(1(1(2(1(1(1(1(1(1(1(0(1(2(1(1(0(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(1(2(2(2(0(0(1(2(0(0(2(2(1(1(2(2(2(1(1(1(0(2(2(2(1(2(1(2(2(0(2(1(1(2(0(1(2(0(0(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(0(1(2(2(1(0(2(1(1(0(0(0(0(1(0(1(2(0(2(1(2(1(0(0(0(0(2(0(2(0(0(2(2(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(1(1(1(0(2(2(0(2(0(1(0(0(1(1(0(1(0(2(0(2(0(2(2(0(1(0(1(2(1(1(2(1(1(0(1(1(2(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(0(1(0(1(1(2(2(2(1(1(2(1(0(1(0(0(1(0(0(1(1(1(2(0(1(2(2(1(1(1(2(2(2(0(1(1(2(0(0(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(x1)))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(1(0(0(1(1(1(1(0(2(2(2(2(2(2(0(2(0(2(2(2(0(1(2(1(0(0(0(2(1(1(0(2(0(0(2(2(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))) -> 2(0(2(1(1(0(2(1(2(1(1(0(2(2(2(1(1(2(1(1(1(2(1(2(2(0(1(1(0(0(1(2(1(0(2(2(1(2(2(1(0(1(0(1(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(0(0(2(0(2(2(0(0(2(0(1(0(0(1(2(0(0(0(0(0(0(1(0(2(0(1(0(2(0(2(2(2(2(1(0(2(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(1(0(0(0(0(2(1(1(1(0(0(2(1(1(1(0(1(1(1(0(0(0(2(0(2(1(0(0(2(1(2(0(2(1(1(2(2(2(0(0(2(1(2(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(1(0(0(2(1(2(1(1(0(2(1(1(0(0(2(0(1(1(1(0(0(0(0(0(1(0(0(2(1(1(1(0(1(0(1(1(2(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(2(2(1(2(2(2(0(2(1(2(1(1(0(2(1(1(1(2(2(0(1(1(1(0(0(1(1(1(0(1(1(2(1(0(2(0(2(1(2(2(1(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(0(2(2(0(2(1(1(1(2(2(0(0(2(2(2(0(0(1(1(0(0(2(0(0(2(2(0(0(0(2(2(0(1(1(1(0(2(0(1(2(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(0(0(2(2(0(0(1(0(2(2(0(0(2(2(0(2(1(0(2(2(0(2(2(1(0(2(2(2(2(0(1(1(2(0(2(2(1(0(0(0(2(0(2(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(1(1(1(0(0(2(0(1(2(0(2(0(0(2(0(2(2(0(1(0(1(1(2(0(1(1(2(0(0(2(1(0(0(1(2(2(1(2(0(2(0(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(1(1(1(0(0(0(0(0(2(2(2(1(2(2(0(2(2(0(0(2(1(1(0(1(2(2(0(1(0(1(1(0(2(1(1(0(1(2(1(2(0(0(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: 0(1(x1)) -> 2(2(1(x1))) 1(1(0(x1))) -> 1(2(2(1(x1)))) 0(2(2(0(0(1(1(x1))))))) -> 1(0(2(2(2(2(2(1(2(1(1(x1))))))))))) 1(0(0(2(1(0(1(x1))))))) -> 0(2(2(2(1(0(2(2(x1)))))))) 0(1(1(0(0(2(0(2(0(1(2(0(x1)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(x1))))))))))))) 1(2(1(0(1(2(2(0(1(1(1(1(x1)))))))))))) -> 1(2(1(2(1(0(2(0(2(2(1(2(0(x1))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(x1))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(x1))))))))))))))))))) 1(0(0(2(0(1(1(1(1(1(2(2(0(0(2(1(1(x1))))))))))))))))) -> 2(1(2(2(2(2(1(1(2(0(2(2(1(1(1(2(0(1(x1)))))))))))))))))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(x1)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(x1))))))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(x1))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(x1))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(x1))))))))))))))))))))) -> 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0(1(1(1(1(1(2(1(0(2(1(1(2(2(0(2(0(0(1(2(0(0(0(0(1(1(2(2(1(1(2(0(2(1(2(1(1(1(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 1(2(2(1(1(0(0(1(2(1(2(0(1(0(0(0(1(1(1(2(2(2(2(1(2(2(1(2(0(0(1(2(0(1(0(1(1(2(2(2(2(0(2(1(0(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(2(0(2(1(1(2(0(0(0(2(0(1(2(2(2(0(0(1(1(2(1(1(1(1(1(1(1(0(1(2(1(1(0(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(1(2(2(2(0(0(1(2(0(0(2(2(1(1(2(2(2(1(1(1(0(2(2(2(1(2(1(2(2(0(2(1(1(2(0(1(2(0(0(0(2(0(x1))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(0(1(2(2(1(0(2(1(1(0(0(0(0(1(0(1(2(0(2(1(2(1(0(0(0(0(2(0(2(0(0(2(2(1(1(0(x1)))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(1(1(1(0(2(2(0(2(0(1(0(0(1(1(0(1(0(2(0(2(0(2(2(0(1(0(1(2(1(1(2(1(1(0(1(1(2(1(1(2(x1))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(0(1(0(1(1(2(2(2(1(1(2(1(0(1(0(0(1(0(0(1(1(1(2(0(1(2(2(1(1(1(2(2(2(0(1(1(2(0(0(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(x1))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(x1)))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(1(0(0(1(1(1(1(0(2(2(2(2(2(2(0(2(0(2(2(2(0(1(2(1(0(0(0(2(1(1(0(2(0(0(2(2(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))) -> 2(0(2(1(1(0(2(1(2(1(1(0(2(2(2(1(1(2(1(1(1(2(1(2(2(0(1(1(0(0(1(2(1(0(2(2(1(2(2(1(0(1(0(1(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(x1)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(x1)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(x1)))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(0(0(2(0(2(2(0(0(2(0(1(0(0(1(2(0(0(0(0(0(0(1(0(2(0(1(0(2(0(2(2(2(2(1(0(2(1(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(1(0(0(0(0(2(1(1(1(0(0(2(1(1(1(0(1(1(1(0(0(0(2(0(2(1(0(0(2(1(2(0(2(1(1(2(2(2(0(0(2(1(2(1(2(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(x1)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(1(0(0(2(1(2(1(1(0(2(1(1(0(0(2(0(1(1(1(0(0(0(0(0(1(0(0(2(1(1(1(0(1(0(1(1(2(0(0(1(x1))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(2(2(1(2(2(2(0(2(1(2(1(1(0(2(1(1(1(2(2(0(1(1(1(0(0(1(1(1(0(1(1(2(1(0(2(0(2(1(2(2(1(0(1(2(0(x1))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(0(2(2(0(2(1(1(1(2(2(0(0(2(2(2(0(0(1(1(0(0(2(0(0(2(2(0(0(0(2(2(0(1(1(1(0(2(0(1(2(1(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(0(0(2(2(0(0(1(0(2(2(0(0(2(2(0(2(1(0(2(2(0(2(2(1(0(2(2(2(2(0(1(1(2(0(2(2(1(0(0(0(2(0(2(0(0(0(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(x1))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(1(1(1(0(0(2(0(1(2(0(2(0(0(2(0(2(2(0(1(0(1(1(2(0(1(1(2(0(0(2(1(0(0(1(2(2(1(2(0(2(0(1(1(1(2(x1)))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(1(1(1(0(0(0(0(0(2(2(2(1(2(2(0(2(2(0(0(2(1(1(0(1(2(2(0(1(0(1(1(0(2(1(1(0(1(2(1(2(0(0(2(0(1(1(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(x1)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(x1)))))))))))))))))))))))))))))))))))))))))))))))))) The (relative) TRS S consists of the following rules: encArg(cons_0(x_1)) -> 0(encArg(x_1)) encArg(cons_1(x_1)) -> 1(encArg(x_1)) encArg(cons_2(x_1)) -> 2(encArg(x_1)) encode_0(x_1) -> 0(encArg(x_1)) encode_1(x_1) -> 1(encArg(x_1)) encode_2(x_1) -> 2(encArg(x_1)) Rewrite Strategy: INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 0(2(2(0(0(1(1(z0))))))) -> 1(0(2(2(2(2(2(1(2(1(1(z0))))))))))) 0(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(z0)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))))) 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2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(z0)))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(z0))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(z0)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(z0))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(z0)))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(z0)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(z0))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(z0))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(z0))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(z0))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(z0)))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(z0)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(z0))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(z0)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(z0)))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(z0))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(z0)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCODE_1(z0) -> c4(1'(encArg(z0)), ENCARG(z0)) ENCODE_2(z0) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(1(z0)) -> c6(2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(2(2(0(0(1(1(z0))))))) -> c7(1'(0(2(2(2(2(2(1(2(1(1(z0))))))))))), 0'(2(2(2(2(2(1(2(1(1(z0)))))))))), 2'(2(2(2(2(1(2(1(1(z0))))))))), 2'(2(2(2(1(2(1(1(z0)))))))), 2'(2(2(1(2(1(1(z0))))))), 2'(2(1(2(1(1(z0)))))), 2'(1(2(1(1(z0))))), 1'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> c8(2'(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))), 2'(2(1(0(0(0(2(1(2(2(2(1(z0)))))))))))), 2'(1(0(0(0(2(1(2(2(2(1(z0))))))))))), 1'(0(0(0(2(1(2(2(2(1(z0)))))))))), 0'(0(0(2(1(2(2(2(1(z0))))))))), 0'(0(2(1(2(2(2(1(z0)))))))), 0'(2(1(2(2(2(1(z0))))))), 2'(1(2(2(2(1(z0)))))), 1'(2(2(2(1(z0))))), 2'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> c9(2'(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))), 1'(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))))))), 2'(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))), 1'(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))))), 0'(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))), 0'(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))), 1'(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))), 0'(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))), 2'(1(2(0(2(2(2(2(1(0(2(z0))))))))))), 1'(2(0(2(2(2(2(1(0(2(z0)))))))))), 2'(0(2(2(2(2(1(0(2(z0))))))))), 0'(2(2(2(2(1(0(2(z0)))))))), 2'(2(2(2(1(0(2(z0))))))), 2'(2(2(1(0(2(z0)))))), 2'(2(1(0(2(z0))))), 2'(1(0(2(z0)))), 1'(0(2(z0))), 0'(2(z0)), 2'(z0)) 0'(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> c10(1'(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))), 2'(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))))))), 1'(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))), 1'(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))))), 2'(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))), 2'(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))), 2'(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))), 1'(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))), 2'(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))), 0'(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))), 1'(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))), 0'(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))), 1'(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))), 2'(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))), 1'(2(0(2(0(1(1(2(2(1(2(z0))))))))))), 2'(0(2(0(1(1(2(2(1(2(z0)))))))))), 0'(2(0(1(1(2(2(1(2(z0))))))))), 2'(0(1(1(2(2(1(2(z0)))))))), 0'(1(1(2(2(1(2(z0))))))), 1'(1(2(2(1(2(z0)))))), 1'(2(2(1(2(z0))))), 2'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> c11(2'(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))), 0'(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))))))), 0'(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))), 2'(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))))), 2'(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))), 1'(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))), 2'(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))), 2'(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))), 1'(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))), 2'(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))), 2'(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))), 2'(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))), 2'(2(0(2(2(1(2(0(1(2(1(z0))))))))))), 2'(0(2(2(1(2(0(1(2(1(z0)))))))))), 0'(2(2(1(2(0(1(2(1(z0))))))))), 2'(2(1(2(0(1(2(1(z0)))))))), 2'(1(2(0(1(2(1(z0))))))), 1'(2(0(1(2(1(z0)))))), 2'(0(1(2(1(z0))))), 0'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> c12(0'(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))), 2'(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))))))))), 2'(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))), 0'(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))))))), 1'(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))), 1'(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))))), 1'(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))), 1'(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))), 0'(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))), 0'(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))), 1'(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))), 1'(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))), 2'(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))), 1'(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))), 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1'(2(1(2(2(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))), 2'(1(2(2(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0)))))))))))))))))))))))))))))))))))))))), 1'(2(2(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))), 2'(2(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0)))))))))))))))))))))))))))))))))))))), 2'(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0))))))))))))))))))))))))))))))))))))), 1'(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0)))))))))))))))))))))))))))))))))))), 2'(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0))))))))))))))))))))))))))))))))))), 1'(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0)))))))))))))))))))))))))))))))))), 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1'(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))), 2'(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))), 0'(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))), 1'(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))), 2'(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))), 1'(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))), 1'(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))), 1'(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))), 1'(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))), 0'(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))), 0'(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))), 1'(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))), 0'(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))), 0'(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))), 1'(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))), 1'(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))), 0'(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))), 2'(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))), 1'(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))), 0'(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))), 0'(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))), 0'(2(2(0(2(1(0(0(0(0(0(z0))))))))))), 2'(2(0(2(1(0(0(0(0(0(z0)))))))))), 2'(0(2(1(0(0(0(0(0(z0))))))))), 0'(2(1(0(0(0(0(0(z0)))))))), 2'(1(0(0(0(0(0(z0))))))), 1'(0(0(0(0(0(z0)))))), 0'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) S tuples: 0'(1(z0)) -> c6(2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(2(2(0(0(1(1(z0))))))) -> c7(1'(0(2(2(2(2(2(1(2(1(1(z0))))))))))), 0'(2(2(2(2(2(1(2(1(1(z0)))))))))), 2'(2(2(2(2(1(2(1(1(z0))))))))), 2'(2(2(2(1(2(1(1(z0)))))))), 2'(2(2(1(2(1(1(z0))))))), 2'(2(1(2(1(1(z0)))))), 2'(1(2(1(1(z0))))), 1'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) 0'(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> c8(2'(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))), 2'(2(1(0(0(0(2(1(2(2(2(1(z0)))))))))))), 2'(1(0(0(0(2(1(2(2(2(1(z0))))))))))), 1'(0(0(0(2(1(2(2(2(1(z0)))))))))), 0'(0(0(2(1(2(2(2(1(z0))))))))), 0'(0(2(1(2(2(2(1(z0)))))))), 0'(2(1(2(2(2(1(z0))))))), 2'(1(2(2(2(1(z0)))))), 1'(2(2(2(1(z0))))), 2'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> c9(2'(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))), 1'(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))))))), 2'(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))), 1'(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))))), 0'(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))), 0'(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))), 1'(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))), 0'(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))), 2'(1(2(0(2(2(2(2(1(0(2(z0))))))))))), 1'(2(0(2(2(2(2(1(0(2(z0)))))))))), 2'(0(2(2(2(2(1(0(2(z0))))))))), 0'(2(2(2(2(1(0(2(z0)))))))), 2'(2(2(2(1(0(2(z0))))))), 2'(2(2(1(0(2(z0)))))), 2'(2(1(0(2(z0))))), 2'(1(0(2(z0)))), 1'(0(2(z0))), 0'(2(z0)), 2'(z0)) 0'(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> c10(1'(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))), 2'(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))))))), 1'(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))), 1'(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))))), 2'(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))), 2'(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))), 2'(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))), 1'(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))), 2'(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))), 0'(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))), 1'(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))), 0'(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))), 1'(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))), 2'(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))), 1'(2(0(2(0(1(1(2(2(1(2(z0))))))))))), 2'(0(2(0(1(1(2(2(1(2(z0)))))))))), 0'(2(0(1(1(2(2(1(2(z0))))))))), 2'(0(1(1(2(2(1(2(z0)))))))), 0'(1(1(2(2(1(2(z0))))))), 1'(1(2(2(1(2(z0)))))), 1'(2(2(1(2(z0))))), 2'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> c11(2'(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))), 0'(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))))))), 0'(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))), 2'(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))))), 2'(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))), 1'(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))), 2'(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))), 2'(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))), 1'(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))), 2'(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))), 2'(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))), 2'(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))), 2'(2(0(2(2(1(2(0(1(2(1(z0))))))))))), 2'(0(2(2(1(2(0(1(2(1(z0)))))))))), 0'(2(2(1(2(0(1(2(1(z0))))))))), 2'(2(1(2(0(1(2(1(z0)))))))), 2'(1(2(0(1(2(1(z0))))))), 1'(2(0(1(2(1(z0)))))), 2'(0(1(2(1(z0))))), 0'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> c12(0'(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))), 2'(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))))))))), 2'(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))), 0'(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))))))), 1'(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))), 1'(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))))), 1'(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))), 1'(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))))), 0'(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))), 0'(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))))), 1'(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))), 1'(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))))), 2'(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))), 1'(1(0(0(2(2(0(2(2(1(2(1(2(z0))))))))))))), 1'(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))), 0'(0(2(2(0(2(2(1(2(1(2(z0))))))))))), 0'(2(2(0(2(2(1(2(1(2(z0)))))))))), 2'(2(0(2(2(1(2(1(2(z0))))))))), 2'(0(2(2(1(2(1(2(z0)))))))), 0'(2(2(1(2(1(2(z0))))))), 2'(2(1(2(1(2(z0)))))), 2'(1(2(1(2(z0))))), 1'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 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1'(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))))))))))))))), 2'(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))), 1'(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))))))))))))), 1'(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))), 0'(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))))))))))), 2'(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))), 0'(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))))))))), 2'(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))), 0'(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))))))), 0'(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))), 0'(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))))), 2'(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))), 2'(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))))), 1'(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))), 0'(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))))))))))))))))))), 1'(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))), 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2'(0(0(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))))), 0'(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))), 0'(2(0(2(1(1(2(1(1(2(1(2(z0)))))))))))), 2'(0(2(1(1(2(1(1(2(1(2(z0))))))))))), 0'(2(1(1(2(1(1(2(1(2(z0)))))))))), 2'(1(1(2(1(1(2(1(2(z0))))))))), 1'(1(2(1(1(2(1(2(z0)))))))), 1'(2(1(1(2(1(2(z0))))))), 2'(1(1(2(1(2(z0)))))), 1'(1(2(1(2(z0))))), 1'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 2'(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> c80(2'(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))), 1'(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))))), 2'(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))), 0'(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))))), 1'(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))), 2'(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))))), 1'(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))), 0'(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))))), 1'(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))), 0'(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))))), 0'(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))), 1'(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))))), 2'(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))), 1'(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))))), 0'(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))), 0'(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))))), 1'(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))), 1'(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))))), 2'(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))), 0'(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))))), 1'(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))), 2'(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))))), 1'(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))), 1'(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))))), 1'(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))), 1'(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))))), 0'(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))), 1'(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))))), 0'(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))), 1'(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))))), 0'(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))), 0'(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))))), 1'(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))), 1'(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))))), 0'(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))), 2'(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))))), 1'(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))), 0'(0(0(2(2(0(2(1(0(0(0(0(0(z0))))))))))))), 0'(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))), 0'(2(2(0(2(1(0(0(0(0(0(z0))))))))))), 2'(2(0(2(1(0(0(0(0(0(z0)))))))))), 2'(0(2(1(0(0(0(0(0(z0))))))))), 0'(2(1(0(0(0(0(0(z0)))))))), 2'(1(0(0(0(0(0(z0))))))), 1'(0(0(0(0(0(z0)))))), 0'(0(0(0(0(z0))))), 0'(0(0(0(z0)))), 0'(0(0(z0))), 0'(0(z0)), 0'(z0)) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, 0'_1, 1'_1, 2'_1 Compound Symbols: c_2, c1_2, c2_2, c3_2, c4_2, c5_2, c6_3, c7_11, c8_13, c9_19, c10_25, c11_23, c12_26, c13_30, c14_30, c15_30, c16_34, c17_35, c18_35, c19_35, c20_36, c21_38, c22_36, c23_44, c24_39, c25_41, c26_40, c27_41, c28_44, c29_44, c30_44, c31_43, c32_49, c33_47, c34_45, c35_47, c36_48, c37_49, c38_50, c39_50, c40_4, c41_8, c42_13, c43_18, c44_23, c45_29, c46_28, c47_30, c48_29, c49_31, c50_30, c51_35, c52_37, c53_42, c54_41, c55_38, c56_43, c57_40, c58_46, c59_41, c60_45, c61_49, c62_44, c63_44, c64_49, c65_50, c66_24, c67_22, c68_30, c69_31, c70_41, c71_32, c72_33, c73_38, c74_47, c75_49, c76_44, c77_44, c78_48, c79_49, c80_50 ---------------------------------------- (7) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 71 leading nodes: 0'(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> c9(2'(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))), 1'(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))))))), 2'(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))), 1'(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))))), 0'(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))), 0'(1(0(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))))), 1'(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))), 0'(2(1(2(0(2(2(2(2(1(0(2(z0)))))))))))), 2'(1(2(0(2(2(2(2(1(0(2(z0))))))))))), 1'(2(0(2(2(2(2(1(0(2(z0)))))))))), 2'(0(2(2(2(2(1(0(2(z0))))))))), 0'(2(2(2(2(1(0(2(z0)))))))), 2'(2(2(2(1(0(2(z0))))))), 2'(2(2(1(0(2(z0)))))), 2'(2(1(0(2(z0))))), 2'(1(0(2(z0)))), 1'(0(2(z0))), 0'(2(z0)), 2'(z0)) 0'(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> c10(1'(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))), 2'(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))))))), 1'(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))), 1'(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))))), 2'(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))), 2'(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))))), 2'(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))), 1'(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))))), 2'(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))), 0'(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))))), 1'(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))), 0'(1(2(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))))), 1'(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))), 2'(1(2(0(2(0(1(1(2(2(1(2(z0)))))))))))), 1'(2(0(2(0(1(1(2(2(1(2(z0))))))))))), 2'(0(2(0(1(1(2(2(1(2(z0)))))))))), 0'(2(0(1(1(2(2(1(2(z0))))))))), 2'(0(1(1(2(2(1(2(z0)))))))), 0'(1(1(2(2(1(2(z0))))))), 1'(1(2(2(1(2(z0)))))), 1'(2(2(1(2(z0))))), 2'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) 0'(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> c11(2'(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))), 0'(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))))))), 0'(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))), 2'(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))))), 2'(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))), 1'(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))))), 2'(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))), 2'(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))))), 1'(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))), 2'(2(2(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))))), 2'(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))), 2'(2(2(0(2(2(1(2(0(1(2(1(z0)))))))))))), 2'(2(0(2(2(1(2(0(1(2(1(z0))))))))))), 2'(0(2(2(1(2(0(1(2(1(z0)))))))))), 0'(2(2(1(2(0(1(2(1(z0))))))))), 2'(2(1(2(0(1(2(1(z0)))))))), 2'(1(2(0(1(2(1(z0))))))), 1'(2(0(1(2(1(z0)))))), 2'(0(1(2(1(z0))))), 0'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> c13(2'(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))))), 1'(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))))))))))))))), 2'(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))), 2'(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))))))))))))), 1'(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))), 0'(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))))))))))), 2'(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))), 1'(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))))))))), 1'(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))), 1'(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))))))), 1'(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))), 1'(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))))), 2'(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))), 1'(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))))), 0'(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))), 1'(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))))), 2'(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))), 2'(1(1(1(2(2(0(2(2(2(1(0(2(z0))))))))))))), 1'(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))), 1'(1(2(2(0(2(2(2(1(0(2(z0))))))))))), 1'(2(2(0(2(2(2(1(0(2(z0)))))))))), 2'(2(0(2(2(2(1(0(2(z0))))))))), 2'(0(2(2(2(1(0(2(z0)))))))), 0'(2(2(2(1(0(2(z0))))))), 2'(2(2(1(0(2(z0)))))), 2'(2(1(0(2(z0))))), 2'(1(0(2(z0)))), 1'(0(2(z0))), 0'(2(z0)), 2'(z0)) 0'(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(z0)))))))))))))))))))))))))))))) -> c14(1'(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))))), 0'(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))))))))))))))), 2'(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))), 1'(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))))))))))))), 1'(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))), 2'(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))))))))))), 0'(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))), 1'(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))))))))), 0'(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))), 2'(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))))))), 0'(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))), 0'(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))))), 2'(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))), 1'(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))))), 1'(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))), 1'(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))))), 1'(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))), 2'(0(0(2(1(0(0(0(2(2(2(2(1(z0))))))))))))), 0'(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))), 0'(2(1(0(0(0(2(2(2(2(1(z0))))))))))), 2'(1(0(0(0(2(2(2(2(1(z0)))))))))), 1'(0(0(0(2(2(2(2(1(z0))))))))), 0'(0(0(2(2(2(2(1(z0)))))))), 0'(0(2(2(2(2(1(z0))))))), 0'(2(2(2(2(1(z0)))))), 2'(2(2(2(1(z0))))), 2'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 0'(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(z0)))))))))))))))))))))))))))))) -> c15(0'(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))))))), 1'(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0))))))))))))))))))))))))))))), 1'(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))))), 1'(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0))))))))))))))))))))))))))), 1'(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))), 1'(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0))))))))))))))))))))))))), 1'(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))), 1'(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0))))))))))))))))))))))), 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c16(1'(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))))))), 2'(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0))))))))))))))))))))))))))))))))), 1'(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))))), 0'(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0))))))))))))))))))))))))))))))), 1'(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))), 1'(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0))))))))))))))))))))))))))))), 1'(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))), 1'(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0))))))))))))))))))))))))))), 2'(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))), 0'(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0))))))))))))))))))))))))), 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2'(1(1(2(0(2(2(2(1(1(2(1(2(1(z0)))))))))))))), 1'(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))), 1'(2(0(2(2(2(1(1(2(1(2(1(z0)))))))))))), 2'(0(2(2(2(1(1(2(1(2(1(z0))))))))))), 0'(2(2(2(1(1(2(1(2(1(z0)))))))))), 2'(2(2(1(1(2(1(2(1(z0))))))))), 2'(2(1(1(2(1(2(1(z0)))))))), 2'(1(1(2(1(2(1(z0))))))), 1'(1(2(1(2(1(z0)))))), 1'(2(1(2(1(z0))))), 2'(1(2(1(z0)))), 1'(2(1(z0))), 2'(1(z0)), 1'(z0)) 2'(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> c77(2'(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))), 1'(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))))))))))))))), 1'(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))), 1'(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))))))))))))), 1'(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))), 1'(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))))))))))), 2'(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))), 0'(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))))))))), 2'(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))), 1'(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))))))), 1'(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))), 1'(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))))), 2'(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))), 0'(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))))), 1'(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))), 1'(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))))), 0'(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))), 2'(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))))), 1'(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))), 1'(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))))), 1'(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))), 2'(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))))), 2'(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))), 1'(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))))), 1'(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))), 2'(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))))), 0'(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))), 2'(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))))), 2'(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))), 2'(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))))), 2'(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))), 2'(2(0(0(0(0(2(2(2(0(2(1(1(z0))))))))))))), 2'(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))), 0'(0(0(0(2(2(2(0(2(1(1(z0))))))))))), 0'(0(0(2(2(2(0(2(1(1(z0)))))))))), 0'(0(2(2(2(0(2(1(1(z0))))))))), 0'(2(2(2(0(2(1(1(z0)))))))), 2'(2(2(0(2(1(1(z0))))))), 2'(2(0(2(1(1(z0)))))), 2'(0(2(1(1(z0))))), 0'(2(1(1(z0)))), 2'(1(1(z0))), 1'(1(z0)), 1'(z0)) Removed 1 trailing nodes: 1'(0(0(2(1(0(1(z0))))))) -> c41(0'(2(2(2(1(0(2(2(z0)))))))), 2'(2(2(1(0(2(2(z0))))))), 2'(2(1(0(2(2(z0)))))), 2'(1(0(2(2(z0))))), 1'(0(2(2(z0)))), 0'(2(2(z0))), 2'(2(z0)), 2'(z0)) ---------------------------------------- (8) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 0(2(2(0(0(1(1(z0))))))) -> 1(0(2(2(2(2(2(1(2(1(1(z0))))))))))) 0(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(z0)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))))) 0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(z0)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))))))) 0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(z0)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))))))) 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2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(z0)))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(z0)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(z0))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(z0))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(z0))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(z0))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(z0)))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(z0)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(z0))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(z0)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(z0)))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(z0))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(z0)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(2'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCODE_1(z0) -> c4(1'(encArg(z0)), ENCARG(z0)) ENCODE_2(z0) -> c5(2'(encArg(z0)), ENCARG(z0)) 0'(1(z0)) -> c6(2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(1(0(z0))) -> c40(1'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(2'(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))), 2'(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))))))))), 1'(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))), 1'(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))))))), 1'(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))), 2'(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))))), 0'(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))), 2'(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))), 2'(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))), 2'(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))), 0'(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))), 2'(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))), 2'(2(1(2(2(1(1(0(2(1(2(z0))))))))))), 2'(1(2(2(1(1(0(2(1(2(z0)))))))))), 1'(2(2(1(1(0(2(1(2(z0))))))))), 2'(2(1(1(0(2(1(2(z0)))))))), 2'(1(1(0(2(1(2(z0))))))), 1'(1(0(2(1(2(z0)))))), 1'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) S tuples: 0'(1(z0)) -> c6(2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(1(0(z0))) -> c40(1'(2(2(1(z0)))), 2'(2(1(z0))), 2'(1(z0)), 1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(2'(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))), 2'(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))))))))), 1'(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))), 1'(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))))))), 1'(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))), 2'(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))))), 0'(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))), 2'(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))))), 2'(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))), 2'(0(2(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))))), 0'(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))), 2'(2(2(1(2(2(1(1(0(2(1(2(z0)))))))))))), 2'(2(1(2(2(1(1(0(2(1(2(z0))))))))))), 2'(1(2(2(1(1(0(2(1(2(z0)))))))))), 1'(2(2(1(1(0(2(1(2(z0))))))))), 2'(2(1(1(0(2(1(2(z0)))))))), 2'(1(1(0(2(1(2(z0))))))), 1'(1(0(2(1(2(z0)))))), 1'(0(2(1(2(z0))))), 0'(2(1(2(z0)))), 2'(1(2(z0))), 1'(2(z0)), 2'(z0)) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, 0'_1, 1'_1 Compound Symbols: c_2, c1_2, c2_2, c3_2, c4_2, c5_2, c6_3, c40_4, c44_23 ---------------------------------------- (9) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 29 trailing tuple parts ---------------------------------------- (10) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 0(2(2(0(0(1(1(z0))))))) -> 1(0(2(2(2(2(2(1(2(1(1(z0))))))))))) 0(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(z0)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))))) 0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(z0)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))))))) 0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(z0)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))))))) 0(2(1(0(1(1(2(0(1(2(1(2(2(0(2(1(1(1(0(1(1(0(2(0(1(1(2(2(1(2(0(2(2(z0))))))))))))))))))))))))))))))))) -> 2(1(2(2(2(2(2(0(2(1(1(1(1(2(0(0(0(2(0(0(2(2(1(1(0(0(1(1(2(1(0(2(1(0(2(z0))))))))))))))))))))))))))))))))))) 0(2(0(1(0(1(0(2(0(0(2(0(2(1(0(0(0(0(0(1(0(2(2(2(0(0(2(0(2(1(1(0(2(2(z0)))))))))))))))))))))))))))))))))) -> 2(2(1(2(0(1(2(0(1(2(2(2(1(1(2(2(2(1(1(2(1(2(2(0(2(2(0(2(1(0(2(0(2(2(0(z0))))))))))))))))))))))))))))))))))) 0(2(2(2(0(0(1(2(0(2(0(0(1(1(2(1(1(0(1(2(0(1(0(1(2(0(2(1(0(0(1(1(2(0(z0)))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(0(2(1(0(0(2(1(2(2(2(1(0(1(0(0(0(0(2(0(1(1(0(2(0(0(1(0(1(0(0(z0))))))))))))))))))))))))))))))))))) 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2(2(1(1(0(1(1(2(1(2(2(1(1(2(2(0(0(0(1(1(1(2(1(2(2(2(0(0(1(2(2(2(1(2(2(2(0(2(2(2(1(2(1(2(2(1(z0)))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(1(2(1(0(1(0(2(1(0(2(1(0(2(0(1(2(0(1(2(0(2(2(2(1(2(1(0(2(1(1(1(1(2(2(0(1(z0)))))))))))))))))))))))))))))))))))))))) -> 1(1(0(2(0(2(2(2(0(1(2(2(2(2(0(2(1(0(1(1(2(2(2(2(1(0(1(1(1(2(1(2(1(0(0(2(1(1(0(0(0(z0))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(2(0(2(1(1(2(0(0(0(2(0(1(2(2(2(0(0(1(1(2(1(1(1(1(1(1(1(0(1(2(1(1(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(1(2(2(2(0(0(1(2(0(0(2(2(1(1(2(2(2(1(1(1(0(2(2(2(1(2(1(2(2(0(2(1(1(2(0(1(2(0(0(0(2(0(z0))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(0(1(2(2(1(0(2(1(1(0(0(0(0(1(0(1(2(0(2(1(2(1(0(0(0(0(2(0(2(0(0(2(2(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(z0)))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(z0))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(z0)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(z0))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(z0)))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(z0)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(z0))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(z0))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(z0))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(z0))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(z0)))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(z0)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(z0))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(z0)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(z0)))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(z0))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(z0)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCODE_0(z0) -> c3(0'(encArg(z0)), ENCARG(z0)) ENCODE_1(z0) -> c4(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) ENCODE_2(z0) -> c5(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) S tuples: 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_0_1, ENCODE_1_1, ENCODE_2_1, 0'_1, 1'_1 Compound Symbols: c_2, c1_2, c3_2, c4_2, c2_1, c5_1, c6_1, c40_1, c44_1 ---------------------------------------- (11) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (12) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 0(2(2(0(0(1(1(z0))))))) -> 1(0(2(2(2(2(2(1(2(1(1(z0))))))))))) 0(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> 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1(1(2(2(2(0(1(1(2(0(2(2(0(0(2(1(1(0(0(1(0(0(1(0(0(0(1(2(2(0(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(0(1(1(2(1(2(2(1(1(2(2(0(0(0(1(1(1(2(1(2(2(2(0(0(1(2(2(2(1(2(2(2(0(2(2(2(1(2(1(2(2(1(z0)))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(1(2(1(0(1(0(2(1(0(2(1(0(2(0(1(2(0(1(2(0(2(2(2(1(2(1(0(2(1(1(1(1(2(2(0(1(z0)))))))))))))))))))))))))))))))))))))))) -> 1(1(0(2(0(2(2(2(0(1(2(2(2(2(0(2(1(0(1(1(2(2(2(2(1(0(1(1(1(2(1(2(1(0(0(2(1(1(0(0(0(z0))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(2(0(2(1(1(2(0(0(0(2(0(1(2(2(2(0(0(1(1(2(1(1(1(1(1(1(1(0(1(2(1(1(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(1(2(2(2(0(0(1(2(0(0(2(2(1(1(2(2(2(1(1(1(0(2(2(2(1(2(1(2(2(0(2(1(1(2(0(1(2(0(0(0(2(0(z0))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(0(1(2(2(1(0(2(1(1(0(0(0(0(1(0(1(2(0(2(1(2(1(0(0(0(0(2(0(2(0(0(2(2(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(z0)))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(z0))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(z0)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(z0))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(z0)))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(z0)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(z0))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(z0))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(z0))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(z0))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(z0)))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(z0)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(z0))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(z0)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(z0)))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(z0))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(z0)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) ENCODE_2(z0) -> c5(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_0(z0) -> c7(ENCARG(z0)) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCODE_1(z0) -> c7(ENCARG(z0)) S tuples: 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, ENCODE_2_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c_2, c1_2, c2_1, c5_1, c6_1, c40_1, c44_1, c7_1 ---------------------------------------- (13) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 3 leading nodes: ENCODE_2(z0) -> c5(ENCARG(z0)) ENCODE_0(z0) -> c7(ENCARG(z0)) ENCODE_1(z0) -> c7(ENCARG(z0)) ---------------------------------------- (14) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 0(2(2(0(0(1(1(z0))))))) -> 1(0(2(2(2(2(2(1(2(1(1(z0))))))))))) 0(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(z0)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))))) 0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(z0)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))))))) 0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(z0)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))))))) 0(2(1(0(1(1(2(0(1(2(1(2(2(0(2(1(1(1(0(1(1(0(2(0(1(1(2(2(1(2(0(2(2(z0))))))))))))))))))))))))))))))))) -> 2(1(2(2(2(2(2(0(2(1(1(1(1(2(0(0(0(2(0(0(2(2(1(1(0(0(1(1(2(1(0(2(1(0(2(z0))))))))))))))))))))))))))))))))))) 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1(1(0(0(2(0(0(0(0(0(0(2(1(2(1(1(1(1(2(2(1(0(0(0(0(1(1(1(1(1(1(2(1(2(0(2(1(0(1(z0))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(2(2(0(0(2(1(0(1(1(0(2(1(2(1(0(2(1(0(0(1(0(1(0(2(0(2(1(1(2(2(0(0(2(2(1(2(z0)))))))))))))))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(0(0(2(1(1(0(0(1(0(0(1(0(0(0(1(2(2(0(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(0(1(1(2(1(2(2(1(1(2(2(0(0(0(1(1(1(2(1(2(2(2(0(0(1(2(2(2(1(2(2(2(0(2(2(2(1(2(1(2(2(1(z0)))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(1(2(1(0(1(0(2(1(0(2(1(0(2(0(1(2(0(1(2(0(2(2(2(1(2(1(0(2(1(1(1(1(2(2(0(1(z0)))))))))))))))))))))))))))))))))))))))) -> 1(1(0(2(0(2(2(2(0(1(2(2(2(2(0(2(1(0(1(1(2(2(2(2(1(0(1(1(1(2(1(2(1(0(0(2(1(1(0(0(0(z0))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(2(0(2(1(1(2(0(0(0(2(0(1(2(2(2(0(0(1(1(2(1(1(1(1(1(1(1(0(1(2(1(1(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(1(2(2(2(0(0(1(2(0(0(2(2(1(1(2(2(2(1(1(1(0(2(2(2(1(2(1(2(2(0(2(1(1(2(0(1(2(0(0(0(2(0(z0))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(0(1(2(2(1(0(2(1(1(0(0(0(0(1(0(1(2(0(2(1(2(1(0(0(0(0(2(0(2(0(0(2(2(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(z0)))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(z0))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(z0)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(z0))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(z0)))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(z0)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(z0))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(z0))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(z0))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(z0))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(z0)))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(z0)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(z0))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(z0)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(z0)))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(z0))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(z0)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) S tuples: 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: 0_1, 1_1, 2_1, encArg_1, encode_0_1, encode_1_1, encode_2_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c_2, c1_2, c2_1, c6_1, c40_1, c44_1, c7_1 ---------------------------------------- (15) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_0(z0) -> 0(encArg(z0)) encode_1(z0) -> 1(encArg(z0)) encode_2(z0) -> 2(encArg(z0)) 0(2(2(0(0(1(1(z0))))))) -> 1(0(2(2(2(2(2(1(2(1(1(z0))))))))))) 0(1(1(0(0(2(0(2(0(1(2(0(z0)))))))))))) -> 2(2(2(1(0(0(0(2(1(2(2(2(1(z0))))))))))))) 0(0(1(2(1(2(1(1(2(2(1(1(2(1(2(0(2(z0))))))))))))))))) -> 2(1(2(1(0(0(1(0(2(1(2(0(2(2(2(2(1(0(2(z0))))))))))))))))))) 0(1(0(0(2(0(1(1(0(0(2(0(0(1(2(0(1(0(0(1(0(z0))))))))))))))))))))) -> 1(2(1(1(2(2(2(1(2(0(1(0(1(2(1(2(0(2(0(1(1(2(2(1(2(z0))))))))))))))))))))))))) 0(2(1(0(2(1(2(0(0(1(2(0(1(1(0(0(1(1(0(1(1(z0))))))))))))))))))))) -> 2(0(0(2(2(1(2(2(1(2(2(2(2(2(0(2(2(1(2(0(1(2(1(z0))))))))))))))))))))))) 0(2(0(2(0(1(0(2(0(2(0(0(1(1(1(1(2(0(1(0(0(2(0(1(1(z0))))))))))))))))))))))))) -> 0(2(2(0(1(1(1(1(0(0(1(1(2(1(1(0(0(2(2(0(2(2(1(2(1(2(z0)))))))))))))))))))))))))) 0(0(2(0(0(0(0(2(1(2(0(0(1(1(1(1(2(2(2(2(2(1(0(1(0(1(0(1(0(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(0(2(1(1(1(1(1(2(1(0(1(2(2(1(1(1(2(2(0(2(2(2(1(0(2(z0)))))))))))))))))))))))))))))) 0(1(0(1(2(2(2(1(2(2(0(0(0(1(1(0(0(2(2(0(2(1(1(1(0(1(0(2(2(1(z0)))))))))))))))))))))))))))))) -> 1(0(2(1(1(2(0(1(0(2(0(0(2(1(1(1(1(2(0(0(2(1(0(0(0(2(2(2(2(1(z0)))))))))))))))))))))))))))))) 0(1(1(0(2(1(2(2(2(0(1(0(2(0(1(1(0(1(1(1(2(0(0(0(2(0(1(2(2(1(z0)))))))))))))))))))))))))))))) -> 0(1(1(1(1(1(1(1(2(2(1(0(2(0(1(0(1(0(2(0(2(2(1(0(2(2(0(2(0(0(z0)))))))))))))))))))))))))))))) 0(1(0(2(1(2(1(0(1(1(0(2(1(0(0(1(1(1(2(2(2(1(1(1(2(2(2(2(2(0(1(2(z0)))))))))))))))))))))))))))))))) -> 1(2(1(0(1(1(1(1(2(0(2(1(2(0(2(2(1(1(0(0(1(0(2(0(2(0(0(0(2(1(0(2(1(2(z0)))))))))))))))))))))))))))))))))) 0(2(1(0(1(1(2(0(1(2(1(2(2(0(2(1(1(1(0(1(1(0(2(0(1(1(2(2(1(2(0(2(2(z0))))))))))))))))))))))))))))))))) -> 2(1(2(2(2(2(2(0(2(1(1(1(1(2(0(0(0(2(0(0(2(2(1(1(0(0(1(1(2(1(0(2(1(0(2(z0))))))))))))))))))))))))))))))))))) 0(2(0(1(0(1(0(2(0(0(2(0(2(1(0(0(0(0(0(1(0(2(2(2(0(0(2(0(2(1(1(0(2(2(z0)))))))))))))))))))))))))))))))))) -> 2(2(1(2(0(1(2(0(1(2(2(2(1(1(2(2(2(1(1(2(1(2(2(0(2(2(0(2(1(0(2(0(2(2(0(z0))))))))))))))))))))))))))))))))))) 0(2(2(2(0(0(1(2(0(2(0(0(1(1(2(1(1(0(1(2(0(1(0(1(2(0(2(1(0(0(1(1(2(0(z0)))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(0(2(1(0(0(2(1(2(2(2(1(0(1(0(0(0(0(2(0(1(1(0(2(0(0(1(0(1(0(0(z0))))))))))))))))))))))))))))))))))) 0(0(0(1(0(2(2(2(0(1(0(0(2(2(2(1(1(0(1(0(2(1(0(0(0(0(1(0(1(2(0(0(2(1(0(z0))))))))))))))))))))))))))))))))))) -> 1(2(2(0(1(2(1(1(2(2(0(2(0(0(2(1(0(0(0(2(1(2(0(2(1(1(2(2(2(2(2(2(2(2(2(1(z0)))))))))))))))))))))))))))))))))))) 0(0(2(2(2(1(1(2(2(2(1(2(1(0(1(0(0(2(2(1(2(1(1(1(1(1(0(2(2(0(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))) -> 0(2(2(2(1(0(0(2(2(0(0(0(0(2(2(2(1(0(2(2(1(0(2(1(2(1(0(2(2(1(2(2(2(0(2(1(1(1(z0)))))))))))))))))))))))))))))))))))))) 0(1(2(1(0(2(1(0(2(0(0(1(1(1(1(1(0(0(0(0(2(1(0(2(1(0(1(2(1(1(2(2(0(1(1(z0))))))))))))))))))))))))))))))))))) -> 2(0(1(1(0(1(2(1(1(1(2(1(2(2(0(2(1(0(1(1(1(1(1(2(1(2(0(2(1(1(1(1(0(0(1(2(z0)))))))))))))))))))))))))))))))))))) 0(1(2(2(0(1(1(2(1(2(0(1(1(0(0(1(1(0(0(0(1(1(0(1(1(1(1(2(1(1(1(1(1(2(0(1(z0)))))))))))))))))))))))))))))))))))) -> 1(2(0(1(2(0(2(2(2(0(2(1(2(0(2(2(2(1(2(1(2(2(1(2(1(2(2(0(2(0(1(0(1(0(0(0(2(1(0(2(1(2(0(1(z0)))))))))))))))))))))))))))))))))))))))))))) 0(0(0(1(1(1(2(0(1(2(2(2(0(2(0(2(0(0(2(2(0(0(0(0(2(0(0(0(0(2(2(0(1(1(1(0(1(z0))))))))))))))))))))))))))))))))))))) -> 1(2(1(1(1(1(2(2(0(0(2(1(1(1(2(0(2(2(0(0(1(2(0(1(2(0(1(1(0(1(2(2(0(2(1(1(0(0(1(z0))))))))))))))))))))))))))))))))))))))) 0(0(0(2(0(0(1(0(0(1(1(1(2(0(0(1(2(0(0(0(0(1(1(0(1(0(2(1(1(1(0(0(0(2(1(0(0(z0))))))))))))))))))))))))))))))))))))) -> 2(2(1(2(2(0(2(0(0(2(1(2(2(1(2(2(2(0(2(2(0(2(0(0(2(1(2(2(2(0(2(1(2(0(2(0(2(1(0(1(1(z0))))))))))))))))))))))))))))))))))))))))) 0(0(1(1(2(2(1(0(0(1(0(1(1(0(0(2(1(1(2(1(1(2(2(2(2(0(0(1(0(1(0(0(1(1(2(2(1(z0))))))))))))))))))))))))))))))))))))) -> 1(2(0(0(2(2(1(1(2(2(1(0(1(2(0(2(1(1(1(2(2(0(0(1(0(2(2(2(0(2(2(2(2(1(2(1(2(2(0(0(z0)))))))))))))))))))))))))))))))))))))))) 0(0(1(0(1(0(1(2(0(0(0(0(0(2(2(1(0(0(2(1(0(0(2(2(0(2(0(0(1(2(0(0(1(2(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(1(1(1(0(0(1(2(0(2(2(2(1(1(0(2(0(1(1(1(2(2(1(1(0(1(2(1(1(2(1(2(2(1(0(1(z0))))))))))))))))))))))))))))))))))))))))) 0(1(0(2(1(0(2(2(0(1(1(1(1(0(0(2(0(2(1(0(0(2(1(0(1(1(0(2(2(0(2(1(2(0(0(2(0(0(z0)))))))))))))))))))))))))))))))))))))) -> 0(0(1(1(2(0(1(1(2(2(0(2(1(1(2(2(2(0(1(0(2(2(1(2(2(0(0(2(1(2(1(2(2(2(2(0(2(2(1(0(2(0(2(2(z0)))))))))))))))))))))))))))))))))))))))))))) 0(0(1(2(1(2(1(0(0(1(1(0(1(0(1(2(0(1(1(1(1(1(1(0(0(1(1(1(0(2(1(2(2(0(0(2(0(1(2(0(z0)))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(0(0(1(1(2(2(1(0(0(1(2(0(2(1(1(2(1(0(0(0(2(1(2(2(2(1(0(0(2(2(0(0(1(1(0(2(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) 0(2(2(1(0(1(2(0(1(1(2(2(1(1(0(2(2(0(1(1(0(0(0(0(1(0(0(1(2(0(2(1(1(0(0(0(1(2(2(1(z0)))))))))))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(0(0(1(0(1(2(1(2(1(2(0(2(0(2(0(0(2(2(0(2(1(0(0(2(2(2(1(2(0(1(1(1(0(0(1(0(0(2(z0)))))))))))))))))))))))))))))))))))))))))))) 0(2(2(0(1(2(1(2(2(0(0(0(1(2(0(1(0(1(1(0(0(0(0(2(1(0(2(1(0(0(1(2(0(0(2(2(1(0(1(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 1(1(1(2(1(2(2(1(2(1(0(2(1(0(1(1(1(2(2(2(1(2(1(0(1(1(2(1(0(1(2(2(2(0(0(0(1(0(0(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))) 0(1(0(0(2(2(0(1(1(1(2(0(2(2(0(1(0(2(0(2(0(0(1(0(2(2(2(2(1(1(1(1(2(2(0(0(2(0(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))) -> 2(0(2(2(0(2(2(2(0(2(1(2(2(1(1(0(2(2(2(1(0(2(0(2(2(2(0(0(2(1(0(2(0(0(0(0(1(2(2(2(1(2(2(0(2(0(2(0(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(1(1(2(1(0(2(1(1(2(2(0(2(0(0(1(2(0(0(0(0(1(1(2(2(1(1(2(0(2(1(2(1(1(1(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 1(2(2(1(1(0(0(1(2(1(2(0(1(0(0(0(1(1(1(2(2(2(2(1(2(2(1(2(0(0(1(2(0(1(0(1(1(2(2(2(2(0(2(1(0(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(1(1(1(0(2(2(0(2(0(1(0(0(1(1(0(1(0(2(0(2(0(2(2(0(1(0(1(2(1(1(2(1(1(0(1(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(0(0(1(0(1(1(2(2(2(1(1(2(1(0(1(0(0(1(0(0(1(1(1(2(0(1(2(2(1(1(1(2(2(2(0(1(1(2(0(0(0(0(1(z0))))))))))))))))))))))))))))))))))))))))))))) 0(1(0(1(1(1(0(0(1(1(1(1(0(2(2(2(2(2(2(0(2(0(2(2(2(0(1(2(1(0(0(0(2(1(1(0(2(0(0(2(2(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(0(2(1(1(0(2(1(2(1(1(0(2(2(2(1(1(2(1(1(1(2(1(2(2(0(1(1(0(0(1(2(1(0(2(2(1(2(2(1(0(1(0(1(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(1(0(1(0(0(2(0(2(2(0(0(2(0(1(0(0(1(2(0(0(0(0(0(0(1(0(2(0(1(0(2(0(2(2(2(2(1(0(2(1(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 1(2(1(0(0(0(0(2(1(1(1(0(0(2(1(1(1(0(1(1(1(0(0(0(2(0(2(1(0(0(2(1(2(0(2(1(1(2(2(2(0(0(2(1(2(1(2(0(z0)))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(0(0(1(0(0(2(1(2(1(1(0(2(1(1(0(0(2(0(1(1(1(0(0(0(0(0(1(0(0(2(1(1(1(0(1(0(1(1(2(0(0(1(z0))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(0(2(2(1(2(2(2(0(2(1(2(1(1(0(2(1(1(1(2(2(0(1(1(1(0(0(1(1(1(0(1(1(2(1(0(2(0(2(1(2(2(1(0(1(2(0(z0))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(2(2(0(2(2(0(2(1(1(1(2(2(0(0(2(2(2(0(0(1(1(0(0(2(0(0(2(2(0(0(0(2(2(0(1(1(1(0(2(0(1(2(1(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(0(0(2(2(0(0(1(0(2(2(0(0(2(2(0(2(1(0(2(2(0(2(2(1(0(2(2(2(2(0(1(1(2(0(2(2(1(0(0(0(2(0(2(0(0(0(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 0(1(1(1(2(1(1(1(0(0(2(0(1(2(0(2(0(0(2(0(2(2(0(1(0(1(1(2(0(1(1(2(0(0(2(1(0(0(1(2(2(1(2(0(2(0(1(1(1(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(1(1(1(0(0(0(0(0(2(2(2(1(2(2(0(2(2(0(0(2(1(1(0(1(2(2(0(1(0(1(1(0(2(1(1(0(1(2(1(2(0(0(2(0(1(1(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(2(1(0(1(z0))))))) -> 0(2(2(2(1(0(2(2(z0)))))))) 1(2(1(0(1(2(2(0(1(1(1(1(z0)))))))))))) -> 1(2(1(2(1(0(2(0(2(2(1(2(0(z0))))))))))))) 1(0(0(2(0(1(1(1(1(1(2(2(0(0(2(1(1(z0))))))))))))))))) -> 2(1(2(2(2(2(1(1(2(0(2(2(1(1(1(2(0(1(z0)))))))))))))))))) 1(1(0(2(0(1(0(1(1(0(1(2(2(1(0(1(1(2(0(1(2(1(2(z0))))))))))))))))))))))) -> 2(2(2(2(0(2(0(0(0(2(1(2(0(1(1(1(0(0(1(2(2(0(0(2(1(2(0(2(1(z0))))))))))))))))))))))))))))) 1(2(1(2(2(0(1(1(0(1(0(2(1(0(1(0(0(1(1(1(2(0(1(0(1(z0))))))))))))))))))))))))) -> 0(2(0(2(1(0(1(0(1(2(1(2(1(2(0(2(0(2(1(0(1(0(0(0(2(1(0(2(z0)))))))))))))))))))))))))))) 1(2(0(1(1(0(0(2(1(0(2(2(1(2(0(0(2(2(0(2(2(0(0(0(1(1(z0)))))))))))))))))))))))))) -> 2(0(0(0(2(2(2(0(0(2(1(0(2(2(0(0(2(1(2(2(1(1(0(0(2(0(0(1(0(0(z0)))))))))))))))))))))))))))))) 1(2(2(0(1(0(2(1(1(0(0(0(0(0(0(0(1(0(0(0(1(2(2(1(2(2(2(z0))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(0(2(2(0(0(0(0(2(1(0(0(0(1(0(2(2(2(0(0(0(2(1(z0))))))))))))))))))))))))))))) 1(2(2(0(1(1(2(1(0(1(0(2(1(1(2(2(2(1(1(1(2(0(2(0(0(1(1(z0))))))))))))))))))))))))))) -> 2(2(1(0(0(2(2(1(2(1(2(2(2(2(1(2(2(2(1(0(2(1(2(0(0(0(0(1(2(1(0(z0))))))))))))))))))))))))))))))) 1(1(0(1(1(0(1(2(0(0(0(1(0(1(0(0(2(2(0(1(1(1(0(2(1(0(1(0(z0)))))))))))))))))))))))))))) -> 1(2(1(1(2(2(1(1(0(2(0(0(1(2(0(0(0(1(2(1(1(0(2(0(0(2(1(0(1(1(z0)))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(0(0(0(2(0(0(2(0(2(1(0(2(1(0(1(2(2(0(1(2(0(0(1(0(1(z0))))))))))))))))))))))))))))))))) -> 0(0(0(2(1(0(2(1(0(2(1(0(2(1(1(2(2(2(1(2(0(0(2(0(0(2(1(1(1(0(2(2(1(0(1(z0))))))))))))))))))))))))))))))))))) 1(1(0(1(1(1(1(2(0(0(0(0(0(0(2(1(0(0(1(2(0(1(1(0(2(0(0(0(2(1(2(1(2(1(0(z0))))))))))))))))))))))))))))))))))) -> 1(0(0(0(0(1(0(2(0(1(1(2(0(2(0(2(0(2(0(0(0(0(2(1(2(2(2(2(2(1(0(0(1(0(0(2(0(z0))))))))))))))))))))))))))))))))))))) 1(1(2(0(1(0(1(0(1(1(0(2(0(2(2(1(0(2(0(0(2(0(1(2(2(0(2(0(0(0(0(1(2(2(0(1(z0)))))))))))))))))))))))))))))))))))) -> 2(1(1(2(0(0(1(2(2(2(1(0(1(2(0(2(1(1(1(0(1(1(1(1(1(2(2(2(2(1(2(0(2(0(2(1(1(2(2(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))) 1(2(1(0(0(1(1(2(2(0(0(1(0(1(2(1(1(1(0(1(2(0(2(1(1(1(1(1(0(1(2(2(2(0(2(0(2(z0))))))))))))))))))))))))))))))))))))) -> 2(2(2(0(2(0(0(2(2(0(2(2(1(2(2(2(1(0(0(1(1(0(0(2(0(2(0(2(1(1(1(1(1(2(1(0(1(2(1(0(1(z0))))))))))))))))))))))))))))))))))))))))) 1(2(2(1(2(1(0(0(1(2(2(1(0(0(1(2(1(0(0(1(0(0(2(1(0(1(0(2(0(2(1(0(0(0(2(0(1(z0))))))))))))))))))))))))))))))))))))) -> 2(0(0(2(1(1(2(1(2(1(1(1(1(0(1(0(2(0(1(2(1(2(2(1(2(2(1(2(2(1(2(1(2(2(0(2(0(0(z0)))))))))))))))))))))))))))))))))))))) 1(0(2(0(1(1(2(1(1(0(1(2(1(0(1(0(1(1(0(2(1(0(1(0(2(1(0(1(1(0(1(1(0(2(1(0(1(2(z0)))))))))))))))))))))))))))))))))))))) -> 1(2(1(1(2(0(1(2(1(0(2(0(0(0(2(2(0(2(2(2(1(2(0(1(0(2(0(1(2(1(2(1(2(1(1(1(2(2(0(0(0(2(2(z0))))))))))))))))))))))))))))))))))))))))))) 1(1(0(0(2(0(0(0(0(0(0(2(1(2(1(1(1(1(2(2(1(0(0(0(0(1(1(1(1(1(1(2(1(2(0(2(1(0(1(z0))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(2(2(0(0(2(1(0(1(1(0(2(1(2(1(0(2(1(0(0(1(0(1(0(2(0(2(1(1(2(2(0(0(2(2(1(2(z0)))))))))))))))))))))))))))))))))))))))) 1(1(2(2(2(0(1(1(2(0(2(2(0(0(2(1(1(0(0(1(0(0(1(0(0(0(1(2(2(0(1(0(1(0(0(0(2(2(1(z0))))))))))))))))))))))))))))))))))))))) -> 2(2(1(1(0(1(1(2(1(2(2(1(1(2(2(0(0(0(1(1(1(2(1(2(2(2(0(0(1(2(2(2(1(2(2(2(0(2(2(2(1(2(1(2(2(1(z0)))))))))))))))))))))))))))))))))))))))))))))) 1(2(1(2(1(2(1(0(1(0(2(1(0(2(1(0(2(0(1(2(0(1(2(0(2(2(2(1(2(1(0(2(1(1(1(1(2(2(0(1(z0)))))))))))))))))))))))))))))))))))))))) -> 1(1(0(2(0(2(2(2(0(1(2(2(2(2(0(2(1(0(1(1(2(2(2(2(1(0(1(1(1(2(1(2(1(0(0(2(1(1(0(0(0(z0))))))))))))))))))))))))))))))))))))))))) 1(2(0(0(2(0(2(1(1(2(0(0(0(2(0(1(2(2(2(0(0(1(1(2(1(1(1(1(1(1(1(0(1(2(1(1(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 0(2(2(1(2(2(2(0(0(1(2(0(0(2(2(1(1(2(2(2(1(1(1(0(2(2(2(1(2(1(2(2(0(2(1(1(2(0(1(2(0(0(0(2(0(z0))))))))))))))))))))))))))))))))))))))))))))) 1(2(0(2(2(2(0(1(2(2(1(0(2(1(1(0(0(0(0(1(0(1(2(0(2(1(2(1(0(0(0(0(2(0(2(0(0(2(2(1(1(0(z0)))))))))))))))))))))))))))))))))))))))))) -> 2(0(0(0(2(1(1(0(1(2(1(1(2(1(1(0(2(2(2(0(0(2(0(2(2(0(2(1(1(2(2(1(1(0(2(0(2(2(0(2(2(1(0(1(2(1(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(0(0(0(2(0(1(2(0(1(1(0(1(1(1(0(2(0(1(1(0(2(1(2(2(0(1(1(2(1(1(0(1(1(1(2(1(2(2(2(2(2(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(0(0(1(0(2(1(2(0(0(1(2(2(0(2(2(1(2(0(1(2(0(1(2(0(0(2(1(1(0(2(0(2(2(2(2(1(0(1(0(0(1(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) 1(0(1(2(0(0(1(1(1(2(1(2(2(0(0(2(0(2(0(1(1(1(2(1(2(1(2(1(1(0(0(1(1(1(2(1(1(0(0(2(2(1(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 1(1(2(1(0(1(1(2(2(1(2(0(2(2(0(2(0(0(2(2(0(2(0(1(2(2(2(2(0(2(0(0(1(2(2(0(2(0(0(2(2(1(1(2(z0)))))))))))))))))))))))))))))))))))))))))))) 1(1(1(0(2(0(2(0(0(0(0(0(0(1(1(2(1(1(2(0(0(0(1(2(0(2(2(1(1(2(0(0(1(2(0(1(1(0(1(1(0(1(2(2(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(0(2(0(1(2(0(1(2(2(2(0(2(2(2(2(1(2(1(1(2(2(2(1(0(1(1(1(0(2(1(1(1(0(1(1(0(2(1(1(2(1(0(0(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 1(0(1(0(0(1(2(0(1(0(1(2(0(2(1(0(2(2(2(0(0(0(0(1(0(0(0(2(0(1(2(1(2(0(1(2(2(2(0(0(0(0(1(1(2(2(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(1(0(2(2(2(0(0(0(0(2(1(0(1(2(1(2(1(2(0(1(2(0(0(0(2(2(2(1(2(0(2(1(0(0(2(0(0(1(0(2(2(2(2(2(0(2(2(z0)))))))))))))))))))))))))))))))))))))))))))))))))) 2(0(0(2(2(1(0(2(1(2(1(0(1(0(2(2(2(0(1(0(1(z0))))))))))))))))))))) -> 0(0(2(0(0(2(2(2(2(2(0(2(0(2(2(0(2(2(2(2(1(1(2(0(z0)))))))))))))))))))))))) 2(2(1(0(0(1(0(1(2(1(0(2(0(1(1(0(1(2(0(0(1(z0))))))))))))))))))))) -> 2(2(0(0(0(0(2(1(0(0(2(2(1(2(2(1(1(0(1(2(0(2(z0)))))))))))))))))))))) 2(2(0(2(2(2(2(2(0(2(0(0(1(2(0(0(1(0(2(2(2(1(2(2(2(1(0(0(1(z0))))))))))))))))))))))))))))) -> 2(1(2(2(1(2(2(0(2(2(2(0(1(2(1(1(2(2(2(2(1(2(1(0(1(0(0(2(1(2(z0)))))))))))))))))))))))))))))) 2(0(0(0(1(0(1(1(0(2(0(2(0(0(1(0(1(2(0(0(0(2(2(0(1(0(1(0(0(1(0(z0))))))))))))))))))))))))))))))) -> 2(0(0(0(0(0(1(1(0(2(2(2(1(0(0(0(0(1(0(1(0(2(0(1(1(0(0(0(1(0(2(z0))))))))))))))))))))))))))))))) 2(0(2(1(1(2(0(2(2(0(1(1(1(0(0(1(0(0(0(1(1(0(0(0(0(0(2(0(1(1(1(z0))))))))))))))))))))))))))))))) -> 2(2(0(0(2(1(2(2(2(2(2(2(2(0(2(0(2(2(2(2(0(2(1(2(2(2(1(2(1(1(2(0(2(2(2(1(1(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) 2(1(2(2(0(0(1(0(1(0(2(1(0(0(1(1(2(1(0(1(1(0(0(0(0(2(1(1(0(1(1(z0))))))))))))))))))))))))))))))) -> 2(1(0(2(2(2(0(2(1(1(2(0(1(0(1(0(0(1(2(2(2(1(2(0(0(1(1(1(0(2(0(0(z0)))))))))))))))))))))))))))))))) 2(1(0(1(2(1(0(1(1(1(2(2(2(1(0(0(0(0(2(1(1(2(0(1(0(0(0(2(0(1(1(0(z0)))))))))))))))))))))))))))))))) -> 2(1(0(2(2(1(1(2(2(1(0(1(0(0(1(2(2(2(2(2(1(0(0(0(0(0(1(2(1(1(2(2(2(z0))))))))))))))))))))))))))))))))) 2(1(0(1(0(2(1(0(2(1(0(2(0(2(2(2(2(0(0(1(0(1(1(2(1(2(0(2(0(0(2(0(0(0(2(0(z0)))))))))))))))))))))))))))))))))))) -> 2(2(2(1(1(2(0(0(1(2(0(1(0(2(0(2(2(2(1(2(2(0(2(1(2(0(0(1(1(0(0(0(0(2(2(0(0(0(z0)))))))))))))))))))))))))))))))))))))) 2(0(0(1(0(0(0(2(2(0(1(2(1(0(1(2(1(2(2(1(1(2(0(0(1(0(2(2(2(2(1(0(2(2(0(0(0(1(2(0(1(z0))))))))))))))))))))))))))))))))))))))))) -> 2(2(2(2(2(1(0(2(1(2(2(1(1(1(2(1(1(1(1(0(1(2(2(2(1(2(0(0(2(2(0(2(1(2(2(1(2(2(0(1(0(0(1(2(1(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))) 2(0(2(0(1(0(0(0(0(0(2(0(2(0(1(0(0(1(1(1(2(0(1(1(0(0(0(0(1(0(0(0(0(2(0(0(0(0(0(1(0(z0))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(2(2(0(2(1(2(0(0(0(1(2(1(2(2(1(2(2(0(0(1(2(2(0(2(0(2(2(1(0(0(1(2(0(0(0(1(2(2(1(2(1(0(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(1(1(0(1(2(2(0(1(0(2(0(2(2(0(1(0(1(0(1(0(1(0(1(2(2(2(0(1(1(2(0(2(1(2(0(2(1(2(1(z0))))))))))))))))))))))))))))))))))))))))) -> 0(0(2(2(0(2(2(2(0(0(0(0(2(2(0(2(0(2(1(1(1(1(2(0(0(2(2(1(0(0(0(0(1(2(0(0(1(0(1(0(1(0(2(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(1(1(0(2(0(0(0(0(2(0(0(2(0(0(1(1(2(1(1(1(2(1(2(2(1(1(2(2(2(0(0(1(0(0(0(1(0(2(1(2(2(1(z0))))))))))))))))))))))))))))))))))))))))))) -> 2(1(1(1(1(1(2(0(2(1(1(1(2(0(1(1(0(2(1(1(1(2(2(1(1(2(0(2(2(2(2(2(2(0(0(0(0(2(2(2(0(2(1(1(z0)))))))))))))))))))))))))))))))))))))))))))) 2(2(0(0(0(2(0(1(2(2(1(2(1(1(2(1(1(2(0(2(1(0(1(2(1(1(2(1(2(1(1(1(2(1(1(1(1(1(0(0(0(2(2(0(z0)))))))))))))))))))))))))))))))))))))))))))) -> 2(2(1(0(2(0(2(2(0(0(2(0(2(1(2(1(0(2(0(1(1(1(2(2(2(0(1(2(0(2(0(2(2(1(0(2(1(1(1(2(0(2(2(1(1(2(0(2(z0)))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(1(2(2(1(1(2(2(1(1(0(2(2(2(0(0(0(1(2(0(2(0(1(0(2(1(1(0(2(1(2(0(0(0(0(1(1(2(0(0(0(0(1(0(z0)))))))))))))))))))))))))))))))))))))))))))))) -> 0(2(0(2(1(1(2(1(1(0(2(0(2(0(0(0(2(2(1(0(1(2(2(2(1(0(0(1(1(0(1(1(0(1(2(2(0(0(2(0(2(1(1(2(1(1(2(1(2(z0))))))))))))))))))))))))))))))))))))))))))))))))) 2(2(2(0(1(1(1(1(2(1(0(1(2(1(1(0(0(2(1(0(1(0(2(1(2(1(0(0(0(0(0(0(0(1(0(2(1(0(0(0(1(1(0(2(1(0(0(0(1(1(z0)))))))))))))))))))))))))))))))))))))))))))))))))) -> 2(1(2(0(1(2(1(0(1(0(0(1(2(1(0(0(1(1(2(0(1(2(1(1(1(1(0(1(0(1(0(0(1(1(0(2(1(0(0(0(2(2(0(2(1(0(0(0(0(0(z0)))))))))))))))))))))))))))))))))))))))))))))))))) ---------------------------------------- (16) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) S tuples: 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c_2, c1_2, c2_1, c6_1, c40_1, c44_1, c7_1 ---------------------------------------- (17) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 0'(1(z0)) -> c6(1'(z0)) We considered the (Usable) Rules:none And the Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) The order we found is given by the following interpretation: Polynomial interpretation : POL(0(x_1)) = [3] + x_1 POL(0'(x_1)) = [2] POL(1(x_1)) = [3] POL(1'(x_1)) = [1] POL(2(x_1)) = 0 POL(ENCARG(x_1)) = [2]x_1 POL(ENCODE_0(x_1)) = [3] POL(ENCODE_1(x_1)) = [1] + x_1 POL(c(x_1, x_2)) = x_1 + x_2 POL(c1(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c40(x_1)) = x_1 POL(c44(x_1)) = x_1 POL(c6(x_1)) = x_1 POL(c7(x_1)) = x_1 POL(cons_0(x_1)) = [1] + x_1 POL(cons_1(x_1)) = [3] + x_1 POL(cons_2(x_1)) = x_1 POL(encArg(x_1)) = [3]x_1 ---------------------------------------- (18) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c_2, c1_2, c2_1, c6_1, c40_1, c44_1, c7_1 ---------------------------------------- (19) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_0(z0)) -> c(0'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(0'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (20) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(0'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c1_2, c2_1, c6_1, c40_1, c44_1, c7_1, c_2 ---------------------------------------- (21) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (22) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c1_2, c2_1, c6_1, c40_1, c44_1, c7_1, c_2, c_1 ---------------------------------------- (23) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_1(z0)) -> c1(1'(encArg(z0)), ENCARG(z0)) by ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(1'(2(encArg(z0))), ENCARG(cons_2(z0))) ---------------------------------------- (24) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(1'(2(encArg(z0))), ENCARG(cons_2(z0))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c7_1, c_2, c_1, c1_2 ---------------------------------------- (25) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (26) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_0(z0) -> c7(0'(encArg(z0))) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c7_1, c_2, c_1, c1_2, c1_1 ---------------------------------------- (27) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_0(z0) -> c7(0'(encArg(z0))) by ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_0(cons_2(z0)) -> c7(0'(2(encArg(z0)))) ---------------------------------------- (28) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_0(cons_2(z0)) -> c7(0'(2(encArg(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_1_1, ENCODE_0_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c7_1, c_2, c_1, c1_2, c1_1 ---------------------------------------- (29) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_0(cons_2(z0)) -> c7(0'(2(encArg(z0)))) ---------------------------------------- (30) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCODE_1(z0) -> c7(1'(encArg(z0))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_1_1, ENCODE_0_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c7_1, c_2, c_1, c1_2, c1_1 ---------------------------------------- (31) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_1(z0) -> c7(1'(encArg(z0))) by ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCODE_1(cons_2(z0)) -> c7(1'(2(encArg(z0)))) ---------------------------------------- (32) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCODE_1(cons_2(z0)) -> c7(1'(2(encArg(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_2, c1_1, c7_1 ---------------------------------------- (33) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_1(cons_2(z0)) -> c7(1'(2(encArg(z0)))) ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_2, c1_1, c7_1 ---------------------------------------- (35) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_0(cons_0(z0))) -> c(0'(0(encArg(z0))), ENCARG(cons_0(z0))) by ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(0'(0(2(encArg(z0)))), ENCARG(cons_0(cons_2(z0)))) ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(0'(0(2(encArg(z0)))), ENCARG(cons_0(cons_2(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_2, c1_1, c7_1 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_2, c1_1, c7_1 ---------------------------------------- (39) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_1(cons_0(z0))) -> c1(1'(0(encArg(z0))), ENCARG(cons_0(z0))) by ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(1'(0(2(encArg(z0)))), ENCARG(cons_0(cons_2(z0)))) ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(1'(0(2(encArg(z0)))), ENCARG(cons_0(cons_2(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_2, c1_1, c7_1 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_2, c1_1, c7_1 ---------------------------------------- (43) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_1(cons_1(z0))) -> c1(1'(1(encArg(z0))), ENCARG(cons_1(z0))) by ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(1'(1(2(encArg(z0)))), ENCARG(cons_1(cons_2(z0)))) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(1'(1(2(encArg(z0)))), ENCARG(cons_1(cons_2(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (45) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_0(cons_0(z0)) -> c7(0'(0(encArg(z0)))) by ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_0(cons_0(cons_2(z0))) -> c7(0'(0(2(encArg(z0))))) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_0(cons_0(cons_2(z0))) -> c7(0'(0(2(encArg(z0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (49) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_0(cons_0(cons_2(z0))) -> c7(0'(0(2(encArg(z0))))) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_1(cons_0(z0)) -> c7(1'(0(encArg(z0)))) by ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_2(z0))) -> c7(1'(0(2(encArg(z0))))) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_2(z0))) -> c7(1'(0(2(encArg(z0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (53) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_1(cons_0(cons_2(z0))) -> c7(1'(0(2(encArg(z0))))) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_1(cons_1(z0)) -> c7(1'(1(encArg(z0)))) by ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCODE_1(cons_1(cons_2(z0))) -> c7(1'(1(2(encArg(z0))))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCODE_1(cons_1(cons_2(z0))) -> c7(1'(1(2(encArg(z0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: ENCODE_1(cons_1(cons_2(z0))) -> c7(1'(1(2(encArg(z0))))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, 0'_1, 1'_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c2_1, c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2 ---------------------------------------- (59) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace ENCARG(cons_2(z0)) -> c2(ENCARG(z0)) by ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: 0'(1(z0)) -> c6(1'(z0)) 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(z0)) -> c6(1'(z0)) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: 0'_1, 1'_1, ENCARG_1, ENCODE_0_1, ENCODE_1_1 Compound Symbols: c6_1, c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2, c2_1 ---------------------------------------- (61) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace 0'(1(z0)) -> c6(1'(z0)) by 0'(1(1(0(y0)))) -> c6(1'(1(0(y0)))) 0'(1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) -> c6(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) 0'(1(1(0(y0)))) -> c6(1'(1(0(y0)))) 0'(1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) -> c6(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples: 0'(1(1(0(y0)))) -> c6(1'(1(0(y0)))) 0'(1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) -> c6(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: 1'_1, ENCARG_1, ENCODE_0_1, ENCODE_1_1, 0'_1 Compound Symbols: c40_1, c44_1, c_2, c_1, c1_1, c7_1, c1_2, c2_1, c6_1 ---------------------------------------- (63) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: 0'(1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) -> c6(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) 0'(1(1(0(y0)))) -> c6(1'(1(0(y0)))) Removed 3 trailing nodes: ENCODE_0(cons_0(cons_1(z0))) -> c7(0'(0(1(encArg(z0))))) ENCODE_0(cons_1(z0)) -> c7(0'(1(encArg(z0)))) ENCODE_0(cons_0(cons_0(z0))) -> c7(0'(0(0(encArg(z0))))) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_1(z0))) -> c(0'(1(encArg(z0))), ENCARG(cons_1(z0))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(0'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(0'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: 1'_1, ENCARG_1, ENCODE_1_1 Compound Symbols: c40_1, c44_1, c_2, c_1, c1_1, c1_2, c7_1, c2_1 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ENCARG(cons_0(cons_1(z0))) -> c(ENCARG(cons_1(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(ENCARG(cons_0(cons_1(z0)))) S tuples: 1'(1(0(z0))) -> c40(1'(z0)) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: 1'_1, ENCARG_1, ENCODE_1_1 Compound Symbols: c40_1, c44_1, c_1, c1_1, c1_2, c7_1, c2_1 ---------------------------------------- (67) CdtForwardInstantiationProof (BOTH BOUNDS(ID, ID)) Use forward instantiation to replace 1'(1(0(z0))) -> c40(1'(z0)) by 1'(1(0(1(0(y0))))) -> c40(1'(1(0(y0)))) 1'(1(0(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0)))))))))))))))))))))) -> c40(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ENCARG(cons_0(cons_1(z0))) -> c(ENCARG(cons_1(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(ENCARG(cons_0(cons_1(z0)))) 1'(1(0(1(0(y0))))) -> c40(1'(1(0(y0)))) 1'(1(0(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0)))))))))))))))))))))) -> c40(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) S tuples: 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) 1'(1(0(1(0(y0))))) -> c40(1'(1(0(y0)))) 1'(1(0(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0)))))))))))))))))))))) -> c40(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: 1'_1, ENCARG_1, ENCODE_1_1 Compound Symbols: c44_1, c_1, c1_1, c1_2, c7_1, c2_1, c40_1 ---------------------------------------- (69) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: 1'(1(0(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0)))))))))))))))))))))) -> c40(1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(y0))))))))))))))))))))) Removed 1 trailing nodes: 1'(1(0(1(0(y0))))) -> c40(1'(1(0(y0)))) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ENCARG(cons_0(cons_1(z0))) -> c(ENCARG(cons_1(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(ENCARG(cons_0(cons_1(z0)))) S tuples: 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44(1'(1(0(2(1(2(z0))))))) K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: 1'_1, ENCARG_1, ENCODE_1_1 Compound Symbols: c44_1, c_1, c1_1, c1_2, c7_1, c2_1 ---------------------------------------- (71) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ENCARG(cons_0(cons_1(z0))) -> c(ENCARG(cons_1(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(ENCARG(cons_0(cons_1(z0)))) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44 S tuples: 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44 K tuples:none Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, ENCODE_1_1, 1'_1 Compound Symbols: c_1, c1_1, c1_2, c7_1, c2_1, c44 ---------------------------------------- (73) CdtRuleRemovalProof (UPPER BOUND(ADD(n^1))) Found a reduction pair which oriented the following tuples strictly. Hence they can be removed from S. 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44 We considered the (Usable) Rules:none And the Tuples: ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ENCARG(cons_0(cons_1(z0))) -> c(ENCARG(cons_1(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(ENCARG(cons_0(cons_1(z0)))) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44 The order we found is given by the following interpretation: Polynomial interpretation : POL(0(x_1)) = 0 POL(1(x_1)) = 0 POL(1'(x_1)) = [1] POL(2(x_1)) = [1] POL(ENCARG(x_1)) = x_1 POL(ENCODE_1(x_1)) = [1] POL(c(x_1)) = x_1 POL(c1(x_1)) = x_1 POL(c1(x_1, x_2)) = x_1 + x_2 POL(c2(x_1)) = x_1 POL(c44) = 0 POL(c7(x_1)) = x_1 POL(cons_0(x_1)) = x_1 POL(cons_1(x_1)) = [1] + x_1 POL(cons_2(x_1)) = x_1 POL(encArg(x_1)) = [1] ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(cons_0(z0)) -> 0(encArg(z0)) encArg(cons_1(z0)) -> 1(encArg(z0)) encArg(cons_2(z0)) -> 2(encArg(z0)) 0(1(z0)) -> 2(2(1(z0))) 1(1(0(z0))) -> 1(2(2(1(z0)))) 1(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> 2(2(1(1(1(2(0(2(2(2(0(2(2(2(1(2(2(1(1(0(2(1(2(z0))))))))))))))))))))))) Tuples: ENCARG(cons_0(cons_2(z0))) -> c(ENCARG(cons_2(z0))) ENCARG(cons_1(cons_2(z0))) -> c1(ENCARG(cons_2(z0))) ENCARG(cons_0(cons_0(cons_2(z0)))) -> c(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_0(cons_0(z0)))) -> c1(1'(0(0(encArg(z0)))), ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_1(cons_0(cons_1(z0)))) -> c1(1'(0(1(encArg(z0)))), ENCARG(cons_0(cons_1(z0)))) ENCARG(cons_1(cons_0(cons_2(z0)))) -> c1(ENCARG(cons_0(cons_2(z0)))) ENCARG(cons_1(cons_1(cons_0(z0)))) -> c1(1'(1(0(encArg(z0)))), ENCARG(cons_1(cons_0(z0)))) ENCARG(cons_1(cons_1(cons_1(z0)))) -> c1(1'(1(1(encArg(z0)))), ENCARG(cons_1(cons_1(z0)))) ENCARG(cons_1(cons_1(cons_2(z0)))) -> c1(ENCARG(cons_1(cons_2(z0)))) ENCODE_1(cons_0(cons_0(z0))) -> c7(1'(0(0(encArg(z0))))) ENCODE_1(cons_0(cons_1(z0))) -> c7(1'(0(1(encArg(z0))))) ENCODE_1(cons_1(cons_0(z0))) -> c7(1'(1(0(encArg(z0))))) ENCODE_1(cons_1(cons_1(z0))) -> c7(1'(1(1(encArg(z0))))) ENCARG(cons_2(cons_2(y0))) -> c2(ENCARG(cons_2(y0))) ENCARG(cons_2(cons_0(cons_1(y0)))) -> c2(ENCARG(cons_0(cons_1(y0)))) ENCARG(cons_2(cons_0(cons_2(y0)))) -> c2(ENCARG(cons_0(cons_2(y0)))) ENCARG(cons_2(cons_1(cons_2(y0)))) -> c2(ENCARG(cons_1(cons_2(y0)))) ENCARG(cons_2(cons_0(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_0(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_0(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_0(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_0(cons_2(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_0(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_0(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_1(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_1(y0))))) ENCARG(cons_2(cons_1(cons_1(cons_2(y0))))) -> c2(ENCARG(cons_1(cons_1(cons_2(y0))))) ENCARG(cons_0(cons_1(z0))) -> c(ENCARG(cons_1(z0))) ENCARG(cons_0(cons_0(cons_0(z0)))) -> c(ENCARG(cons_0(cons_0(z0)))) ENCARG(cons_0(cons_0(cons_1(z0)))) -> c(ENCARG(cons_0(cons_1(z0)))) 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44 S tuples:none K tuples: 1'(1(1(1(1(2(1(0(2(1(1(1(1(2(0(0(2(2(2(2(z0)))))))))))))))))))) -> c44 Defined Rule Symbols: encArg_1, 0_1, 1_1 Defined Pair Symbols: ENCARG_1, ENCODE_1_1, 1'_1 Compound Symbols: c_1, c1_1, c1_2, c7_1, c2_1, c44 ---------------------------------------- (75) SIsEmptyProof (BOTH BOUNDS(ID, ID)) The set S is empty ---------------------------------------- (76) BOUNDS(1, 1)